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LOGARITHMIC 


AND    OTHER 


MATHEMATICAL     TABLES 


BY 

WILLIAM    J.    HUSSEY 

ASTRONOMER   IN- THE   LICK   OBSERVATORY 


FIFTH    EDITION 


ALLYN   and    BACON 

Boston  anti  (Sljicaga 


ENCJNEERJNG  LIBRARY 

Copyright,  1891, 
By  The  Register  Publishing  Company 

Copyright,  1895, 
By  William  J.  Hussey. 


.da 


PREFACE. 


The  extended  calculations  required  by  some  of  the  applications  of 
trigonometry  are  laborious  even  to  experienced  computers,  and  to  begin- 
ners are  often  a  fruitful  source  of  discouragement.  Experience  in  making 
calculations  and  familiarity  with  the  formulas  employed  suggest  methods 
of  arrangement  by  which  skilful  computers  shorten  their  work  and  save 
much  of  their  time.  The  aim  should  always  be  to  secure  the  results  to  the 
required  degree  of  accuracy  with  a  minimum  expenditure  of  time  and  labor. 
So  far  as  the  mechanical  part  of  the  work  is  concerned,  the  principal  factors 
leading  to  this  end  are  the  proper  arrangement  of  the  formulas  employed, 
the  use  of  conveniently  arranged  tables  having  the  needed  helps  for  facili- 
tating interpolation,  and  the  use  of  no  more  places  of  decimals  than  are 
necessary  to  secure  the  desired  accuracy  in  the  results. 

Orderly  arrangement  is  almost  indispensable  to  correct  and  rapid  com- 
putation; on  this  account  the  practice  of  making  computations  on  scraps 
of  paper  without  systematic  arrangement  should  not  be  followed.  In  the 
beginning,  an  outline  of  the  entire  solution  should  be  made  by  writing  the 
symbols  of  the  quantities  to  be  used  in  a  vertical  column,  those  to  be 
combined  being  placed  adjacent.  In  the  same  solution,  turning  more  than 
once  to  the  same  place  in  the  tables  should  be  avoided,  by  taking  at  one 
opening  all  the  functions  of  a  given  angle  that  may  be  required,  and  writing 
them  in  their  proper  places.  The  tables  employed  should  be  conveniently 
arranged,  and,  in  general,  should  have  auxiliary  tables  of  proportional  parts 
on  the  margins  of  the  pages,  so  that  the  interpolations  can  easily  be  made 
mentally. 

The  number  of  decimal  places  to  be  used  in  any  calculation  is  governed 
by  the  character  of  the  data  given,  and  the  degree  of  accuracy  required 
in  the  results.  When  the  data  have  great  precision,  and  the  results  are 
required  with  all  attainable  accuracy,  seven  decimal  places  must  be  used, 
or  even  a  larger  number.  But  for  nearly  all  calculations  such  precision 
is  not  required,  and  the  use  of  logarithms  to  five  places  of  decimals  is  suffi- 
cient, as  they  afford  results  which  are  generally  correct  to  one  ten-thousandth 


M171605 


part.  In  calculations  where  this  degree  of  accuracy  is  not  necessary,  a  still 
smaller  number  of  decimal  places  may  be  used.  In  such  cases  natural 
numbers  and  the  natural  trigonometric  functions  are  frequently  more  con- 
venient than  their  logarithms. 

In  compiling  this  book  for  general  use,  the  needs  of  computers  and  of 
students  have  been  kept  in  view.  The  arrangements  of  the  tables  are  those 
which  have  been  found  the  most  convenient  by  experienced  computers ; 
they  are  at  the  same  time  such  as  are  best  adapted  to  the  use  of  stu- 
dents. All  needed  helps  are  given  for  facilitating  interpolation.  Aux- 
iliary tables  of  proportional  parts  accompany  the  logarithmic  portions  of 
the  book,  but  are  omitted  in  the  table  of  natural  trigonometric  functions, 
where  differences  are  generally  small. 

Throughout  the  greater  part  of  the  book  every  tenth  line  is  enclosed 
by  parallel  rules,  and  the  other  lines  are  grouped  in  threes.  This  gives  the 
pages  an  open  appearance,  enabling  one  to  find  more  readily  the  numbers 
sought,  and  securing  in  the  trigonometric  tables  a  symmetrical  arrangement 
such  that  the  order  is  the  same  in  reading  from  the  bottom  of  the  page  as 
from  the  top. 

The  auxiliaries  S  and  T,  which  are  always  used  in  connection  with 
the  logarithms  of  numbers,  are  conveniently  placed  at  the  bottom  of 
pages  2  to  21,  instead  of  in  a  separate  table.  Their  arithmetical  comple- 
ments, CS  and  CT,  are  to  be  found  on  pages  62  to  64,  adjacent  to  the 
logarithmic  trigonometric  functions  with  which  they  are  used. 

The  tables  of  addition  and  subtraction  logarithms  are  based  on  those 
of  Zech.  The  argument  in  each  of  these  tables  is  obtained  by  subtract- 
ing the  smaller  logarithm  from  the  larger.  The  function  is  always  added 
to  the  larger  logarithm  in  addition,  and  always  subtracted  from  it  in 
subtraction.  On  account  of  these  uniform  ways  of  proceeding,  these  tables 
are  more  convenient  than  the  Gaussian  tables. 

Note  to  the  Fifth  Edition. 
The  changes  in  this  edition  are  as  follows :  Some  of  the  astronomical 
constants  at  the  end  of  the  book  have  been  altered  to  bring  them  into 
agreement  with  the  results  of  recent  investigations.  The  values  of 
log  tan  10°  24',  log  sin  26°  49',  and  log  tan  30°  13'  have  been  corrected. 
No  other  errors  in  the  third  and  fourth  editions  have  come  to  my  notice. 

W.  J.  HUSSEY. 
Mr.  Hamilton,  California, 
March,  1907. 


CONTENTS. 


PAGE. 

Introduction, vii 

Kules  for  the  use  of  Logarithms,         ........  vii 

Common  Logarithms,        ...........        vii 

Mantissae  of  Common  Logarithms,    ........  viii 

Characteristics  of  Common  Logarithms,     .......  viii 

The  Arithmetical  Complement  of  a  Logarithm,     .....  viii 

Explanations  of  the  Tables, ix 

The  Logarithms  of  Numbers,        .........  1-  22 

Common  Logarithms  of  Numbers  from  1  to  1000,     .        .       .       .       .2-3 

"      100  to  10000,       .        .        .        .  4-21 

Proportional  Parts, 4-  21 

Auxiliaries  S  and  T,        .        .        .        .        .        .        .       .  '    .  2-21 

Natural  Logarithms  of  Whole  Numbers  from  1-200      ....  22 

Addition  and  Subtraction  Logarithms,         ......  23-  36 

Proportional  Parts 24-  36 

Explanatory  Formulas, .  24-  36 

Logarithms  of  the  Trigonometric  Functions,                                     •  37-106 

For  the  First  and  Last  Degrees  of  all  Quadrants,        ...  37-  46 

Proportional  Parts, ....  38-  49 

For  the  next  Five  Degrees  for  all  Quadrants,       .       .        .       .        .  50-60 

Proportional  Parts, 50-  60 

For  the  entire  Circumference  from  Minute  to  Minute,        .       .  61-106 

Differences  and  Proportional  Parts,       ......  62-106 

Auxiliaries  C  S  and  C  T,       .        .        .       .        .       .        .       .  62-64 

Natural  Trigonometric  Functions,    ........  107-130 

Squares,  Cubes,  Square  Roots  and  Cube  Roots,     .                      .  131-139 

Factors  for  Computing  Probable  Errors,     ......  140 

Trigonometric  Formulas, •  141-142 

General  Formulas, 141 

Formulas  Relating  to  Plane  Triangles .  141 

"               "            "    Spherical  Triangles, 142 

Formulas  Resulting  from  the  Method  of  Least  Squares,  .       .  143-145 
Formulas  for  the  Combination  of  Observations  and  the  Determina- 
tion of  Probable  Errors, *43 

Constants, 146-148 

Mathematical  and  Astronomical  Constants, 146 

Comparison  of  Linear  Measures,        ...                ....  146 

Dimensions  of  the  Earth  according  'to  Bessel,      .....  147 


VI  CONTENTS. 

Dimensions  of  the  Earth  according  to  Clarke, 147 

Constants  for  Conversion  of  English  Weights  and  Measures  to  Metric,  and  vice  versa   147-148 

Linear, 147 

Square, 147 

Cubic, 147 

Capacity, 147 

Weight, 148 

Velocity, 148 

Force, 148 

Stress, 148 

Work, 148 

Rate  of  Doing  Work, 148 

Physical  Constanta, 148 


INTRODUCTION. 


Logarithms  are  used  in  lengthy  numerical  calculations  to  diminish  the  labor 
of  multiplication,  division,  involution  and  evolution,  by  respectively  substituting 
for  them  the  operations  of  addition,  subtraction,  multiplication  and  division. 

The  rules  for  their  use  are  as  follows: 

The  logarithm  of  a  product  is  equal  to  the  sum  of  the  logarithms  of  its 
factors. 

The  logarithm  of  a  quotient  is  equal  to  the  logarithm  of  the  dividend,  minus 
the  logarithm  of  the  divisor. 

The  logarithm  of  any  power  of  a  number  is  equal  to  the  logarithm  of  the 
number  multiplied  by  the  index  of  the  power. 

The  logarithm  of  any  root  of  a  number  is  equal  to  the  logarithm  of  the  number 
divided  by  the  index  of  the  root. 

Or,  expressed  in  formulas, 

log4X-B  =  log4  +  log.B,  log^     =log4— log.B, 

log  A»        =n  log  A,  log  %A  =  l^A. 

These  rules  are  true  for  all  systems  of  logarithms.  The  Common  Logarithms 
are  the  only  ones  used  in  numerical  calculations  and  in  the  following  pages  they  are 
always  meant  unless  the  contrary  is  stated. 

The  common  logarithm  of  a  given  number  is  the  index  of  that  power  of  10 
which  is  equal  to  the  number.  Thus,  2  is  the  logarithm  of  100,  because  102  =  100 ; 
this  equation  is  usually  written  log  100  =  2.  10  is  the  base  of  the  system.  A  system 
of  logarithms  comprises  the  logarithms  of  all  positive  numbers  to  a  given  base. 

From  the  definition  of  common  logarithms  it  follows,  that 

logl       =     0,  log  0.1       =  — 1, 

log  10     =  +  1,  log  0.01     =  —  2, 

log  100   =  +  2,  log  0.001   =  —  3, 

log  1000  =  +  3,  log  0.0001  =  —  4, 

etc.,  etc., 

from  which  it  is  evident,  that  logarithms  are,  in  general,  not  integers.    Thus,  the 
logarithm  of  a  number  between 

0.01  and       0.1  is  —  2  +  a  fraction, 

0.1    and       1  is  —  1  -f  a  fraction, 

1      and     10  is      0  -f  a  fraction, 

10      and    100  is      1  +  a  fraction, 

100      and  1000  is      2  + a  fraction. 

The  fractional  part  of  a  logarithm  is  usually  expressed  decimally  and  is  so 
taken  as  to  be  positive.  It  is  then  called  the  mantissa,  and  the  integral  part  is  called 
the  characteristic, 

vii 


Viii  INTRODUCTION. 

Changing  the  decimal  point  in  a  number  is  equivalent  to  multiplying  or 
dividing  it  by  an  integral  power  of  10;  consequently,  the  logarithms  of  numbers 
which  are  the  same,  excepting  the  position  of  the  decimal  point,  differ  by  integers. 
Thus  the  logarithm  of  389.4  is  2.59040,  and  since  38940  =  100  X  389.4,  the  first  rule  for 
the  use  of  logarithms  gives 

log  38940  =  log  100  + log  389.4 

=      2       +2.59040  =  4.59040. 
Similarly, 

log  3.8940  =  log  .01  +  log  389.4 

=    —2    +2.59040  =  0.59040. 
Hence, 

The  mantissae  of  the  logarithms  of  all  numbers  composed  of  the  same  figures 
in  the  same  ordei;  are  the  same. 

The  value  of  the  characteristic  depends  upon  the  position  of  the  decimal 
point  in  the  number.    An  inspection  of  the  above  table  shows,  that 

The  characteristic  of  the  logarithm  of  a  number,  partly  or  wholly  integral,  is 
zero  or  positive,  and  one  less  than  the  number  of  figures  in  the  integral  portion ; 

The  characteristic  of  the  logarithm  of  a  pure  decimal  is  negative,  and  one 
more  than  the  number  of  ciphers  preceding  the  first  significant  figure. 

Examples:  The  mantissae  of  the  logarithms  of  349600,  3496,  3.496,  .003496  are 
the  same,  being  .54357;  their  characteristics  are +5, +3,0  and— 3,  respectively. 
Thus,  log  .003496  =  3.54357,  the  minus  sign  being  placed  over  the  characteristic  to 
indicate  that  it  only  is  negative. 

The  rule  given  above  for  determining  the  characteristic  of  the  logarithm  of  a 
pure  decimal  is  strictly  correct,  and  so  also  is  the  manner  of  writing  the  negative 
characteristic.  In  computing,  however,  it  is  not  desirable  to  use  the  characteristics 
in  the  manner  indicated.  It  is  preferable  to  add  10  to  logarithms  having  negative 
characteristics  and  to  allow  for  the  increase  by  a  proper  interpretation  of  the  results. 
When  so  increased  the  characteristics  may,  in  all  operations,  except  in  some  cases 
in  the  extraction  of  roots,  be  treated  as  if  they  were  positive.  When  written  in  this 
manner,  the  rule  for  their  determination  is  as  follows: 

TJie  characteristic  of  the  logarithm  of  a  pure  decimal  is  9,  diminished  by  the 
number  of  ciphers  'preceding  the  first  significant  figure. 

Examples:  The  characteristics  of  the  logarithms  of  .8437,  .02804,  .000105  and 
.000009207  are  respectively  9,  8,  6  and  4. 

The  logarithmic  trigonometric  functions,  and  the  logarithms  of  constants  less 
than  unity  contained  in  these  tables,  have  had  their  characteristics  increased  bv  10. 

In  finding  the  logarithm  of  a  root  an  apparent  difficulty  arises  when  the  char- 
acteristic is  negative  and  is  not  a  multiple  of  the  index  of  the  root.  The  difficulty 
disappears  by  increasing  the  characteristic  negatively  by  the  smallest  number  which 
will  make  it  such  a  multiple  and  by  increasing  the  mantissa  positively  by  the  same 
number.  Thus,  the  logarithm  of  .003392  is  3.53046.  The  logarithm  of  its  square 
root  is  obtained  by  writing  its  logarithm  in  the  form  — 4+  1.53046  and  dividing  by  2, 
the  index  of  the  root.    This  gives  —  2  +  .76523,  or  2.76523,  or  8.76523. 

A  better  way  of  proceeding  is  to  add  10  times  the  index  of  the  root  to  the  log- 
arithm and  then  divide  by  the  index  of  the  root.  Thus,  in  the  example  given,  adding 
20  to  the  logarithm  of  .003392  and  dividing  by  2,  gives  8.7652:*,  which  is  the  logarithm 
of  the  square  root.  By  adding  30  and  dividing  by  3,  the  logarithm  of  the  cube  root 
is  Obtained.    The  logarithm  of  the  cube  root  of  .003392  is  9.17682. 

Tin-  arithmetical  complement  of  a  logarithm  is  the  difference  obtained  by 
subtracting  it  from  0,  or  from  10,  If  it  is  desired  to  avoid  negative  characteristics! 


/ 


INTRODUCTION.  ix 

It  is  easily  obtained  by  subtracting  each  figure  of  the  logarithm,  except  the  last 
significant  one,  from  9;  the  last  significant  figure  must  be  subtracted  from  10. 
Thus,  log  2783  =  3.44138,  and  its  arithmetical  complement  is  6.55862.  It  is  to  be 
noticed,  that  the  logarithm  of  the  reciprocal  of  a  number,  is  the  arithmetical  com- 
plement of  the  logarithm  of  the  number;  for  example,  log  ^^  =  6.55862. 

Since  the  sine  and  cosecant,  cosine  and  secant,  tangent  and  cotangent  are 
reciprocals,  their  logarithms  are  arithmetical  complements.  Thus,  log  sin  22°  18' 
24"=  9.57928,  and  log  cosec  22°  18'  24"=  0.42072;  log  cos  22°  18'  24"=  9.96622,  and 
log  sec  22°  18'  24"=0.03378;  log  tan  22°  18'  24"=  9.61306,  and  log  cot  22°  18'  24"= 
0.38694. 

A  dash  printed  over  a  terminal  5  indicates  that  the  true  value  is  less  than  5. 
For  example  the  logarithm  of  59903  to  seven  decimal  places  is  4.7774486;  to  five 
decimal  places  this  is  written  4.77745.  If  only  four  decimal  places  are  required  in  a 
computation,  the  5  is  neglected.     Thus,  the  above  logarithm  is  written  4.7774. 

When  a  dash  is  not  printed  over  a  terminal  5,  and  only  four  decimal  places 
are  required,  the  fourth  decimal  figure  is  increased  by  one  and  the  5  neglected.  For 
example,  the  logarithm  of  7671  to  five  decimal  places  is  3.88485;  to  four  decimal 
places  this  is  written  3.8849. 

Table  I. 

Pages  2-3  contain  the  mantissae  of  the  logarithms  of  all  numbers  of  one,  two 
and  three  figures;  the  characteristics  are  determined  by  the  rules  previously  given. 
If  the  number  has  one  or  two  figures,  it  is  given  in  the  first  column,  headed  X,  and 
the  mantissa  of  its  logarithm  is  directly  opposite  it  in  the  second  column,  headed  L. 
Thus,  log  3  =0.47712,  log  24  =  1.38021,  log  .067  =  8.82607.  If  the  number  has  three 
figures,  the  first  two  are  given  in  the  first  column  and  the  third  in  the  horizontal 
row  at  the  top  or  bottom  of  the  page,  and  the  mantissa  of  its  logarithm  is  at  the 
intersection  of  the  line  containing  the  first  two  figures  and  the  column  containing 
the  third.    Thus,  log  184  =  2.26482,  log  89.1  =  1.94988,  log  9.37  =  0.97174. 

Pages  4-21  contain  the  mantissae  of  the  logarithms  of  numbers  from  100  to 
10009.  The  arrangement  is  similar  to  that  just  described.  The  first  three  figures  of 
the  number  are  given  in  the  first  column  and  the  fourth  in  the  horizontal  row  at 
the  top  or  bottom  of  the  page.  The  last  three  figures  of  the  mantissae  are  given  in 
the  columns  headed  0,  1,  2,  3,  4,  5,  6,  7,  8,  9,  and  the  first  two.  at  intervals,  in  the 
second  column  under  L.  When  the  first  two  are  not  given  in  any  line,  they  are  to 
be  taken  from  the  first  line  above  containing  them,  except,  when  the  last  three  are 
preceded  by  a  *,  in  which  case  they  are  to  be  taken  from  the  next  line.  Thus,  (p.  13) 
log  5764  =  3.76072,  log  58.35  =  1.76604,  log  .5889  =  9.77004. 

When  the  number  has  more  than  four  figures,  its  logarithm  is  found  by  inter- 
polation. For  small  differences,  it  is  assumed,  that  differences  between  numbers 
are  proportional  to  the  differences  between  their  logarithms.  For  example,  required 
the  logarithm  of  168.342.  The  number  has  three  orders  of  integers,  hence  the 
characteristic  is  2.  Disregarding  the  decimal  point,  the  number  is  168342.  The 
round  numbers,  having  four  significant  figures,  next  smaller  and  next  greater  than 
this,  are  168300  and  168400,  and  their  mantissae  are  (p.  5)  .22608  and  .22634.  These 
numbers  differ  by  100,  their  mantissae,  by  26.  26,  being  the  difference  between  two 
successive  values  in  the  table,  is  the  tabular  difference.  168342  is  42  greater  than 
168300,  hence  its  mantissa  is  -fifa  of  26  (=  11,  to  the  nearest  integer,)  greater  than  that 
of  168300.    Therefore,  log  168.342  =  2.22619.    Similarly,  log  39.6427  =  1.59816. 


X  INTRODUCTION. 

To  facilitate  interpolation,  the  tenths  of  the  tabular  differences  are  given 
under  P  P,  (proportional  parts).    Thus,  from  the  proportional  table  for  26,  (p.  5), 
the  proportional  part  for  4   =  10.4 
&  "  «      «     2=     .52 

Therefore,  "  "      "   42  =  10.92, 

or  11,  to  the  nearest  integer,  which  agrees  with  the  value  above. 

By  reversing  these  operations,  the  number  corresponding  to  a  given  logarithm 
may  be  found.  For  example,  find  the  number  of  which  1.47384  is  the  logarithm. 
The  next  smaller  mantissa  (p.  7)  is  .47378.  It  corresponds  to  the  number  2977.  The 
difference  between  it  and  the  next  greater  mantissa,  .47392,  is  14,  while  the  differ- 
ence between  it  and  the  given  mantissa  is  6.  The  figures  following  2977  are  obtained 
by  dividing  6  by  14,  giving  43.  Hence,  the  number  is  29.7743.  The  interpolation  is 
facilitated  by  using  the  proportional  table  for  14.  In  it,  5.6  is  the  value  next  smaller 
than  the  given  difference  6;  4,  the  fifth  figure  of  the  number,  corresponds  to  5.6. 
The  difference  between  6  and  5.6  is  .4,  which  becomes  4.0  by  removing  the  decimal 
point  one  place  to  the  right.  Corresponding  to  4.0,  the  nearest  value  is  3,  this  is  the 
sixth  figure  of  the  number.  The  interpolations,  where  proportional  parts  are  given, 
should  be  made  mentally,  the  results  only  being  written. 

The  logarithmic  sines  and  tangents  of  small  angles  may  be  found  by  means  of 
the  values  of  S  and  T,  given  at  the  bottoms  of  the  pages.  The  formulas  for  their  use 
are  as  follows: 

log  sin  =  log  arc  +  S, 
log  tan  =  log  arc  +T, 
the  angle  being  expressed  in  seconds  of  arc.    The  value  of  S  or  T,  to  be  used  in  any 
case,  is  that  which  corresponds  to  the  angle. 
Example  1.    Find  log  sin  3".4785. 

log  3.4785  =  0.54139  .  p.  8. 
S  =  4.68557    p.  2. 
log  sin  3".4785  =  5.22696. 
Example  2.    Find  log  tan  1°  14'  17".84  =  log  tan  4457".84. 
log  4457".84  =  3.64912    p.  10. 
T=  4.68564    p.  10. 
log  tan  1°  14'  17".84  =  8.33476. 

Table  II. 
When  the  logarithms  of  two  numbers  are  given  and  the  logarithm  of  their  sum 
or  difference  is  required,  it  may  be  found  by  using  the  addition  or  subtraction  table 
The  equations  at  the  bottoms  of  the  pages,  24-36  inclusive,  indicate  the  manner  of 
using  these  tables.  In  interpolating,  it  is  to  be  noticed  that  the  function  B  decreases 
as  the  argument  A  increases;  consequently,  the  proportional  parts  must  be  sub- 
tracted instead  of  added. 

Example  1.    Given,  log  a  =  0.98519  and  log  b  =  0.64834.    Required  log  (a  +  6). 

log  a  =  0.98519 

log  b  =  0.64834 

A  =  log  a  —  log  b  =  0.33685 

B=  0.16448    p.  24. 
log  (a  +  b)  =  log  a  +  B  =  1.14967. 
In  this  case  the  tabular  difference  is  31,  the  proportional  table  for  31  gives  26 
as  the  proportional  part  corresponding  to  85,  the  last  two  figures  of  A  ;  subtracting 


INTRODUCTION.  Xl 

26  from  0.16474,  the  value  of  B  in  the  table  corresponding  to  a  value  of  A  =  0.33600, 
gives  0.16448.    This  is  the  value  of  B  corresponding  to  A  =  0.33685. 
Example  2.    Given,  log  a  and  log  b,  as  in  Example  1.    Kequired  log  (a —  b). 
In  this  case  x  =  log  a  — log  b  is  >.3,  and,  as  above, 
A  =  log  a  —  log  b  =  0.33685 

B  =  0.26794    p.  29. 
log  (a  —  b)  =  log  a  —  B  =  0.71725. 

Example  3.    Given,  log  a  =  0.74346  and  log  b  =  0.59484.    Required  log  (a — 6). 
In  this  case  x  =  log  a  — log  b  is  <.3,  and 

B  =  log  a— log  b  =  0.14862 

A  =  0.53790    p.  33. 
log  (a—  b)  =  log  a— A  =  0.20556. 

Tables  III  and  IV. 
These  tables,  pp.  37-106,  contain  the  logarithms  of  the  trigonometric  functions. 
The  headings  of  the  pages  and  columns  indicate  what  they  contain.  The  degrees 
are  given  at  the  tops,  and  bottoms,  of  the  pages.  On  pp.  37-49,  the  minutes  and  each 
ten  seconds  are  given  in  columns  at  the  left  and  right,  headed  '  //,  and  the  odd 
seconds  are  given  in  a  horizontal  row  at  the  top  and  bottom  of  each  page.  On 
Pp.  50-106,  the  minutes  are  given  in  columns  at  the  left  and  right,  headed  ' ;  and  on 
pp.  50-60,  each  ten  seconds  is  given  in  a  horizontal  row  at  the  fop  and  bottom  of  each 
page.  The  columns  of  minutes  on  the  left  read  downward;  the  horizontal  rows  at 
the  top,  from  left  to  right;  these  go  with  the  degrees  at  the  tops  of  the  pages.  The 
columns  of  minutes  at  the  right  and  the  horizontal  rows  at  the  bottom,  read  in  the 
opposite  directions,  and  go  with  the  degrees  at  the  bottoms  of  the  pages.  On  pp.  62- 
106,  the  tabular  differences  of  the  logarithmic  sines  and  cosines  are  given  in  the 
columns  headed  d  (difference),  and  those  of  the  logarithmic  tangents  and  cotangents 
in  the  columns  headed  c  d  (common  difference). 
Example  1.    Find  log  sin  0°  37'  24".37. 

Page  44.  log  sin  0°  37'  24"     =  8.03659      Tabular  difference  =  19. 

proportional  part  for  3   =  5.7 

&  "  "     "    7=  1.33 

log  sin  0°  37'  24".37  =  8.03666. 
The  tabular  difference  is  19  and  the  proportional  table  for  19  (p.  45),  is  used  to 
facilitate  the  interpolation.  The  tabular  difference  is  obtained  by  subtracting  log 
sin  0°  37'  24'  =  8.03659  from  log  sin  0°  37'  25"  =  8.03678.  In  performing  this  subtrac- 
tion, only  the  final  figures  of  the  logarithms  need  be  used.  Thus,  in  this  case,  sub- 
tract 59  from  78.  The  interpolation  should  be  made  mentally  and  only  the  final 
result  written. 
Example  2.    Find  log  tan  0°  42'  17".48. 

'   Page  47.  log  tan  0°  42' 17"      =8.08992      Tabular  difference  =  17. 

proportional  part  for  .48  =  8.16 

log  tan  0°  42'  17".48  =  8.09000. 
Example  3.    Find  log  cos  0°  57'  19". 

This  is  given  without  interpolation  in  the  first  column  of  page  48,  the  first 
figures  being  given  at  the  top  of  the  column.    The  value  is  9.99994. 
Example  4.    Find  log  cos  89°  43'  26".4. 

Page  40.  log  cos  89°  43'  26"    =  7.68296     Tabular  difference  =  44. 

proportional  part  for  4  =         17.6 
log  cos  89°  43'  26".4  =  7.68278. 


Xll  INTRODUCTION. 

The  proportional  part  is  subtracted,  because  the  cosine,  here,  decreases  as  the 
angle  increases. 
Example  5.    Find  log  sin  3°  27'  44".6. 

Page  54.  log  sin  3°  27'  40"    =  8.78083     Tabular  difference  =  35. 

proportional  part  for  4       =         14.0 
A  "  "     "         6=  2.1 

log  sin  3°  27'  44".6  =  8.78099. 
Also  from  pages  54  and  55, 

log  cos  3°  27'  44".6  =  9.99920. 
log  tan  3°  27'  44".6  =  8.78178. 
Example  6.    Find  log  tan  8°  33'  17".4. 

Page  70.  log  tan  8°  33'  00"    =  9.17708     Tabular  difference  =  86 

proportional  part  for  10       =         14.3 
"     "    7       =         10.0 
A  "  "     "         4=  .57 

log  tan  8°  33'  17".4  =  9.17733. 

Example  7.    Find  log  cot  56°  43'  24".7. 

Page  95.  log  cot  56°  43'  00"    =  9.81721     Tabular  difference  =  28. 

proportional  part  for  20       =  9.3 

"     "      4        =  1.9 

fr  "  "     "  7=  .33 

log  cot  56°  43'  24".7  =  9.81709. 
When  the  logarithm  of  a  trigonometric  function  is  given,  the  angle  may  be 
found  by  reversing  the  above  operations. 
Example  8.    Given,  log  tan  x  =  9.87258.    Find  x. 

In  the  column  of  logarithmic  tangents  on  page  98,  we  find  log  tan  36°  42'  = 
9.87238,  with  the  tabular  difference  26.    The  difference  between  this  logarithm  and 
the  given  one  is  20.    The  proportional  table  for  26  gives 
proportional  part  for  40      =17.3 
"     "    6      =   2.6 
TV  "  "      "       2    =     .09 

consequently  "  "     "  46.2   =  19.99,  or  very  nearly  20. 

Hence  the  number  of  seconds  is  46.2,  and  the  required  angle  is  36°  42'  46".2. 

When  a  very  small  angle  is  to  be  found  by  means  of  its  logarithmic  sine  or 
tangent,  and  accuracy  is  desired,  the  arithmetical  complement  of  S  or  T,  pp.  2-21, 
should  be  used.  These  are  given  in  the  columns  headed  C  S  and  C  T,  pp.  62-64. 
The  formulas  for  their  use  are  as  follows: 

log  arc  =  log  sin  +  C  S, 
log  arc  =  log  tan  +  CT, 
the  angle  being  expressed  in  seconds  of  arc.    The  value  of  C  S  or  C  T  to  be  used  in 
any  case,  is  that  which  corresponds  to  the  angle. 
Example  9.    Given,  log  sin  x  =  6.82973.    Find  x. 

The  value  of  x,  (see  p.  62),  lies  between  0°  2'  and  0°  3',  or  between  120"  and 
180",  and,  corresponding  to  this, 

C  S  =  5.31443 
log  sin  x  =  6.82«.t7:5 
log  arc  =  2.1441 6. 
The  number  corresponding  to  the  logarithm  2.14416  is,  (p.  4),  139.3fi8.    There- 
fore, x  =  189".368  =  0   2'  L9".868. 


INTRODUCTION. 


It  is  sometimes  required  to  find  the  logarithm  of  one  trigonometric  function 
from  that  of  another,  without  requiring  the  angle.    To  facilitate  this,  special  pro- 
portional tables,  headed  with  the  tabular  differences  of  both  functions,  are  given, 
(pp.  71-106),  wherever  the  space  admits  it. 
Example  10.    Given,  log  tan  x  =  9.67644.    Kequired  log  cos  x. 

The  difference  between  the  given  logarithm  and  that  given  in  the  table, 
9.67622,  (see  p.  87,  opposite  25°  230,  is  22-  The  tabular  differences  of  the  two 
logarithmic  functions  at  this  place  are  32  and  6.  In  the  proportional  table  for  A,  22 
corresponds  to  4;  this,  subtracted  from  the  tabular  logarithmic  cosine  9.95591,  gives 
the  required  log  cos  x  =  9.95587. 

In  the  examples  already  given,  the  angles  have  all  been  less  than  90°.  The 
logarithms  of  trigonometric  functions  of  angles  greater  than  90°  may  be  obtained  by 
remembering  the  relations  given  in  the  following  table: 


Angle 

Sine 

Cosine 

Tangent 

Cotangent 

X 

-f-sina; 

-j-cosa; 

-(-tan* 

-4- cot  X 

90°+jb 

-{-cos  a? 

—  sin  a; 

—  cot  X 

—  tana; 

180°+  x 

—  sin  x 

—  cos  a; 

+  tanaj 

-4-  cot  X 

270°+  x 

—  cos  a; 

-4-  sin  x 

—  cot  X 

—  tan  x 

For  angles  greater  than  90°,  the  degrees  are  given  at  the  tops  and  bottoms  of 
the  pages  in  smaller  type.  Where  these  have  been  obtained  from  the  acute  angle 
on  the  same  page,  by  adding  90°  or  270°,  they  are  preceded  by  a  *.  This  indicates 
that  the  co-function  is  to  be  taken.  Otherwise,  the  direct  function  is  to  be  taken. 
The  algebraic  signs  of  the  functions,  as  indicated  by  the  above  table,  must  be 
attended  to. 

Example  11.    Find  log  sin  112°  15' 17". 

Page  84.  log  sin  112°  15'  00"  =  9.96640     Tabular  difference  =  6. 

proportional  part  for  17"  =  2,  nearly, 

log  sin  112'  15'  17"  =  9.96638. 

From  the  same  page,  log  tan  202°  28' 34"  =  9.61671,  log  cos  202°  28' 34"= 

9.96569„,  log  cot  292°  18'  37"  =  9.61314„. 

In  the  last  two  examples  the  „  following  the  logarithm  indicates  that  the 
trigonometric  function  is  negative.  This  is  the  usual  way  of  indicating  that  the 
number  corresponding  to  a  logarithm  is  negative. 

Table  Y. 
Pages  108-130  contain  the  natural  trigonometric  functions  for  each  minute. 
The  arrangement  is  the  same  as  that  of  the  logarithms  of  the  trigonometric  func- 
tions, pp.  62-106,  except  that  differences  and  proportional  parts  are  not  given. 

Table  VI,  Etc. 
Pages  131-139  contain  the  squares,  cubes,  square  roots  and  cube  roots  of 
numbers  from  1  to  1020.    The  arrangement  of  this  table,  and  also  of  the  ones  which 
follow  it,  will  be  understood  by  inspecting  them. 


I 

TABLE  OF  THE  COMMON 

LOGARITHMS  OF  NUMBERS 

WITH  THE  AUXILIARIES  S  AND  T. 


0—50 


N 

L  0    1 

3   I   4 

5      6      7   |   8     9 

0 

i 

—  00     00  000 

30  103 

47712 

60  206 

69897  |  77S15  |  84510  |  90309  |  95424 

00000 
30103 

47  712 

04139 
32  222 
49136 

07918 
34  242 
50  515 

11  394 
36  173 
51  851 

14613 
38021 
53M8 

17  609 
39  794 
54  407 

20412 
41497 
55  630 

23045 
43  136 
56820 

25  527 
44  716 
57  978 

27875 
46  240 
59  106 

4 
5 
6 

60206 
69897 
77  815 

61278 
70  757 
78  533 

62  325 
71  600 
79239 

63  347 
72428 
79  934 

64  345 
73  239 
80618 

65  321 
74036 
81  291 

66  276 
74819 
8i954 

67  2IO 

75  587 
82607 

68  124 
76  343 
83251 

69020 

77085 
83885  ' 

7 

S 

9 
10 

ii 

12 

13 

84510 
90  309 
95  424 

85126 
90849 
95  904 

85  733 
91  381 
96  379 

86332 
91  908 
96848 

86923 
92428 
97  313 

87  506 
92  942 

97  772 

88081 
93  450 
98227 

88649 
93  952 

98677 

89  209 
94  448 
99  [23 

89763 
94  939 

99  564 

00000 

00432 

00860 

01  284 

01  703 

02  119 

02  531 

02  93S 

03342 

03  743 

04139 
07918 

11  394 

04532 
08  279 
11  727 

04922 
08636 
12057 

05  308 
08  991 
12385 

05  690 
09342 
12  710 

06070 
09  691 
13033 

06446 
10037 
13  354 

06  819 
10  380 
13  672 

07  188 
10  721 
13988 

07  555 
11  059 
14  301 

16 

14  6i3 
17609 
20412 

14922 
17898 
20  683 

15  229 

18  184 
20952 

15  534 
iS  409 
21  219 

15836 

18752 
21  484 

16  137 
I9033 
21748 

16  435 
19  312 
22  on 

16  732 
19  590 
22  272 

17026 
19866 
22  531 

I73I9 
20  140 
22  789 

17 
18 
19 
20 

21 

23 

2304! 
25  527 
-'7  875 

23  300 
25768 
28  103 

23  553 
26007 
28330 

23  805 
26  245 
28556 

24055 
264S2 
28  780 

24  304 
26717 
29003 

24  551 
26951 
29  226 

24  797 
27184 
29  447 

25  042 
27  416 
29  667 

25285 
27  646 
298S5 

3, ,  1 . ,3 

30  320 

30  535 

30750 

30963 

3i  175 

31387 

3i  597 

31  806 

32015 

32  222 
34  242 
30  173 

32428 

34  439 
36  361 

32634 
34  635 
36  549 

32  838 
34S30 
36736 

33041 

35025 
36  922 

33  244 
35  218 
37  107 

33  445 
35  4ii 
37291 

33646 
35603 

37  475 

33846 
35  793 
37658 

34  044 

35  984 
37  840 

24 

25 
26 

38  02I 

39  794 
4i  497 

38  202 

39  967 
41  664 

38382 

40  140 

41  830 

38561 
40  312 
4i  996 

38  739 
40483 
42  160 

38917 
40654 
42325 

39094 
40  824 

42488 

39270 
40  993 
42651 

39  445 

41  162 

42  S13 

39  620 
41330 
42  975 

27 
28 

29 
30 

3i 

32 

33 

43  136 
44716 
46  240 

43  297 
44871 
46389 

43  457 
45025 
46  538 

43616 

45  179 
46687 

43  775 
45  332 
46835 

43  933 
45  484 
46982 

44091 
45  637 
47  129 

4424S 
45788 
47276 

44  404 

45  939 
47422 

44560 

46  090 

47  567 

47  712 

47  857 

4S  001 

48144 

48287 

48430 

48572 

4§  7U 

48855 

48996 

49  136 
5051! 
51  851 

49276 
50651 
51983 

49  415 
507S6 
52  114 

49  554 
50920 
52244 

49  693 
5105! 
52  375 

49831 

51  188 

52  504 

49  969 
51  322 

52634 

50  106 
51455 
52  763 

50243 
5J  |8j 

52  892 

50  379  * 
5i  720 
53  020 

34 
35 
36 

53M8 
54  4«7 
55630 

53  275 

54  531 

55  751 

53  403 

54  654 

55  871 

53  529 

54  777 

55  991 

53656 
54  900 
56  no 

53  782 
55023 
56  229 

53  9o8 

55  145 

56  348 

54  033 

55  267 

56467 

54  158 

55  3^ 
5658! 

542S3 
55  509 
56703 

37 
38 
39 
40 

4i 

42 
43 

56820 
57  978 
59  106 

56  937 

58  092 

59  218 

57  054 
58206 
59  329 

57  171 

58  320 

59  439 

57287 

58  433 

59  550 

57  403 
58546 
59  660 

57  519 
58659 

5'>77" 

57  634 
59  879 

57  749 
59988 

57864 
58  995 
60097 

60  206 

60  314 

60423 

60  531 

60638 

60  746 

60853 

60959 

61  066 

61  172 

61  278 
62325 
63  347 

61384 
62428 
63  448 

61  490 

62531 
63  548 

61  595 

62  634 
63649 

61  700 
62737 
63  749 

61  805 

62  839 
63849 

61  909 

62  941 

63  949 

62  0 1 4 
63043 
64048 

62  118 

63  144 

64  147 

62  221 

63  246 
i>4  246 

44 
45 
46 

64  345 
65321 
66276 

64  444 
65418 
66370 

64542 

65  514 

66  464 

64  640 

65  610 
66558 

64  738 

65  706 
66652 

64836 

66745 

64  933 
65896 
66839 

65  031 
65992 
66932 

65  128 
660S7 
67  025 

65225 
66  181 

"7  ii7 

47 
48 
49 
50 

67  210 

68  124 

67  302 
68215 
69  108 

67  394 
68305 

<><)  i')7 

67486 
68  395 
69285 

67  578 
68485 
69  373 

67  669 

68574 

69461 

67  761 
68664 
69  548 

67852 

68  753 

(h)  i.;,t. 

67  943 

68842 

69723 

68034 
68931 

1  u  1  8  1  n 

69  897 

6998  i 

70070 

70157 

70243 

7..  12„ 

7<>  n: 

70  501 

70586 

70672 

\ 

L0 

1 

2 

3 

4 

(5 

' 

9 

60"  =o°  r   S  4.68557  T  4.68  557 

300"  =0°5'  S  4.68557  T  4-'"  558 

120  =0  2     4.68  557   4.68  557 

360  =06     4.68  557    4.68  558 

180   =0  3       4.68557     4.68  557 

420  =07     4.68  557    4.68  558 

240     0  4       4-',s  55  7     4-<lS  558 

480  =08     4-<>s  557     4-68  558 

50— 

-100 

N 

L0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

50 

5i 
52 
53 

69897 

69  984 

70070 

70157 

7"  2.4.; 

70329 

70415 

70501 

70586 

70672 

70  757 

71  600 
72428 

70842 
71684 
72509 

70927 

71  767 

72  591 

71  012 
71  850 

72673 

71  096 
71933 

72  754 

71  1S1 

72  016 

72835 

71265 
72099 
72916 

7i  349 
72  181 
72  997 

71433 
72  263 
73078 

71  5i7 

72  346 

73  159 

54 

55 
56 

73  239 
74036 
74819 

73320 
74  115 
74896 

73400 
74194 
74  974 

73480 
74  273 
75051 

73  56o 

74  351 

75  128 

73640 
74429 
75205 

73  719 

74  507 
75282 

73  799 

74  586 

75  358 

73878 

74  663 

75  435 

73  957 

74  74i 

75  5ii 

57 
58 
59 
60 

61 
62 
63 

75  587 

76  343 
77085 

75664 
76418 
77  159 

75  740 
76492 
77232 

75815 
76567 
77  305 

75891 
76641 
77  379 

75967 
76716 

77  452 

76042 
76790 

77  525 

76  118 
76864 

77  597 

76  193 
76938 
77670 

76268 

77012 

77  7)  ? 

77815 

77887 

77960 

78  032 

78  104 

78176 

78247 

78319 

78390 

78462 

78  533 
79239 

79  934 

78  604 

79  309 
80003 

78675 

79  379 
80072 

78746 

79  449 

80  140 

78817 

79  518 

80  209 

78  888 

79  588 
80277 

78958 
79  657 
80346 

79029 
79  727 
80414 

79099 
79  796 

80482 

79169 
79  865 
80550 

64 

65 
66 

8061S 
Si  291 
Si  954 

80686 
8135S 
82  020 

8o754 
81  425 
82086 

80821 

81  491 

82  151 

80889 
81558 
82  217 

80956 
81  624 
82282 

81  023 

81  690 

82  347 

81  090 

81  757 

82  413 

81  158 
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•  =o°  33'  S  4-68557  T  4-68559 

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=0  34    4.68  557     4.68  559 

2340  =0  39    4.68  557 

4-68  550 

2100 

=0  35    4  68  557     4.68  559 

2400  =0  40    4.68557 

4-68  559 

2l6c 

=0  36    4.68  557     4.68  559 

2460  =0  41     4.68  556 

4. 68  560 

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=0  37    4.68  557     4.68  559 

2520  =0  42    4.68  556 

4. 68  560 

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4.68 

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300—350 


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324 

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3540  =0  59 

4.68555     4.68562 

350—400 


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369 
370 

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703 

714 

726 

738 

750 

761 

773 

785 

797 

808 

3 
4 
5 
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820 

832 

844 

855 

867 

879 

891 

902 

914 

926 

937 

949 

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972 

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372 

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113 

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148 

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171 

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374 

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299 

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426 

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449 

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473 

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496 

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530 

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553 

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657 

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104 

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138 

149 

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184 

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382 

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297 

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5 

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320 

331 

343 

354 

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377 

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399 

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433 

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512 

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7 

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546 

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670 

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771 

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995 

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12 


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726 > "  —  2'  1 '  S 

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702 

0  =  1  57     4.68  549     4.68  574 

7320  =2  2 

1.68  548     4.68  576 

70? 

0  =  I  58     4.68  549     4-68  575 

7380  =2  3 

i.t.s  548     4.6S 

714 

0  =  1  59     4-68  549     4-'»s  575 

7440  =  2  4 

4.6S  548     (.68  576 

72c 

>o  =  2   0     4.68  549     4.68  575 

7500  =  2  5 

4-68  577 

17 


750- 

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750 

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87  506 

512 

518 

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535 

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57o 

576 

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587 

593 

599 

604 

610 

616 

752 

622 

628 

633 

639 

645 

651 

656 

662 

668 

674 

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679 

685 

691 

697 

703 

708 

714 

720 

726 

731 

754 

737 

743 

749 

754 

760 

766 

772 

777 

783 

789 

755 

795 

800 

806 

812 

818 

823 

829 

835 

841 

846 

756 

852 

858 

S64 

869 

875 

881 

887 

892 

898 

904 

757 

910 

915 

921 

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933 

938 

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967 

973 

978 

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759 
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761 

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030 

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116 

121 

127 

133 

138 

144 

150 

156 

161 

167 

173 

178 

1 84 

190 

762 

195 

201 

207 

213 

218 

224 

230 

235 

241 

247 

6 

763 

252 

258 

264 

270 

275 

281 

287 

292 

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349 

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360 

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765 

366 

372 

377 

383 

389 

395 

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3 

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766 

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429 

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440 

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468 

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767 

480 

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525 

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5 

3-0 

768 

536 

542 

547 

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3-6 

769 
770 
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593 

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610 

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627 

632 

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8 

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5-4 

649 

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840 

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852 

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863 

868 

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137 

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780 

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154 

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209 

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221 

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232 

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265 

271 

276 

282 

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315 

782 

321 

326 

332 

337 

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360 

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371 

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783 

376 

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387 

393 

398 

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409 

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784 

432 

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459 

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470 

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481 

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603 

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620 

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631 

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642 

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788 

653 

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664 

669 

675 

680 

686 

691 

697 

702 

789 
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74i 

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752 

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763 

768 

774 

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790 

796 

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807 

812 

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823 

829 

834 

840 

845 

851 

856 

862 

867 

792 

873 

878 

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889 

894 

900 

905 

911 

916 

922 

793 

927 

933 

938 

944 

949 

955 

960 

966 

971 

977 

794 

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993 

998 

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795 

90037 

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075 

080 

086 

796 

091 

097 

102 

108 

113 

119 

124 

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135 

140 

797 

146 

151 

157 

162 

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173 

179 

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189 

195 

798 

200 

206 

211 

217 

222 

227 

233 

238 

244 

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800 

255 

260 

266 

271 

276 

282 

287 

293 

298 

304 

309 

3i4 

320 

325 

331 

336 

342 

347 

352 

358 

N 

L  0 

1 

2  .  |  3  |  4 

5  |  6  |  7 

8  |  9 

P  P 

7500"  =2°  5'  S  4-68548  T  4-68577 

7Soo"=2°io'  S  4-68  547  T  4-68578 

7560  =26     4.68  548    4.68  577 

7860  =  2  n     4-68  547     4-68579 

7620  =27     4.68  548    4.68  577 

7920  =2  12     4.68  547     4.68  579 

7680  =28     4.68  547    4.68  578 

7980  =  2  13      4-68  547     4-68  579 

7740  =29     4.68  547    4.68  578 

8040  =  2  14     4.68  546     4.68  579 

IS 


^00- 

-850 

N 

L  0  1  1  |  2 

3  |  4 

5 

6 

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800 

90  309 

3M 

320 

325 

33i 

336 

342 

347 

352 

353 

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363 

369 

374 

380 

335 

390 

396 

401 

407 

412 

802 

417 

423 

428 

434 

439 

445 

450 

455 

461 

466 

S03 

472 

477 

482 

488 

493 

499 

504 

509 

5i5 

520 

804 

526 

531 

536 

542 

547 

553 

558 

563 

569 

574 

805 

580 

585 

590 

596 

601 

(in; 

612 

617 

623 

628 

806 

634 

639 

644 

650 

655 

660 

666 

671 

677 

682 

S07 

687 

693 

698 

703 

709 

714 

720 

725 

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736 

808 

741 

747 

752 

757 

763 

768 

773 

779 

784 

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S09 
810 
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795 

800 

806 

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816 

822 

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832 

838 

843 

6 

849 

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859 

865 

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875 

881 

886 

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897 

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907 

913 

918 

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929 

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940 

945 

950 

S12 

956 

961 

966 

972 

977 

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988 

993 

998 

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06 

813 

91  009 

014 

020 

025 

030 

036 

041 

046 

052 

057 

1.2 

814 

062 

068 

073 

078 

084 

089 

094 

100 

105 

no 

3 

1.8 

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116 

121 

126 

132 

137 

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164 

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169 

174 

180 

185 

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265 

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275 

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819 

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821 

328 

334 

339 

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360 

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381 

387 

392 

397 

403 

408 

413 

418 

424 

429 

434 

440 

445 

450 

455 

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466 

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477 

482 

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492 

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514 

519 

524 

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535 

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545 

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630 

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645 

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693 

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730 

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740 

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766   772 

777 

782 

737 

793 

798 

828 

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808 

814 

819   824 

829 

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345 

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861 

866 

871 

876 

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887 

892 

897 

903 
955 

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908 

9*3 

918 

924 

929 

934 

939 

944 

950 

960 

965 

97i 

976 

981 

986 

991 

997 

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832 

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018 

023 

028 

033 

038 

044 

049 

054 

059 

833 

065 

070 

o75 

080 

085 

091 

096 

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IO6 

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3 

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834 

117 

122 

127 

132 

137 

M3 

148 

153 

153 

163 

4 
5 
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169 

174 

179 

184 

189 

195 

200 

205 

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215 

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836 

221 

226 

231 

236 

241 

247 

252 

257 

262 

267 

817 

273 

278 

283 

288 

293 

298 

304 

309 

314 

319 

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324 

330 

335 

340 

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361 

366 

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8 

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376 

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410 

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438 

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464 

469 

474 

480 

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500 

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521 

526 

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531 

536 

542 

547 

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562 

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572 

578 

843 

583 

588 

593 

598 

603 

609 

614 

619 

624 

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639 

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650 

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660 

665 

670 

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696 

701 

706 

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716 

722 

727 

732 

846 

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742 

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752 

758 

763 

768 

773 

778 

733 

847 

788 

793 

799 

804 

809 

814 

819 

824 

829 

834 

848 

840 

84s 

850 

855 

860 

865 

870 

875 

881 

886 

849 
850 

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896 

901 

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916 

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927 

932 

937 

988 

942 

947  I  952 

957 

91.2 

'!<■: 

973 

973 

983 

N 

L  0  |  1  1  2  |  3 

4 

5 

6 

7  1  8  |  9 

P  P 

798 

y  =2°  13'  s  4-68547  T  4.68  57c 

8280' =2°  18'  S  4-68546  T  4-68581 

804 

a  =2  14    4-68546     4-68  57c 

>   8340  —  2     19    4-68  546     4-68  581 

810 

j  =2  15    4-68546     4.6858c 

>   8400  =2  20    4-68545     4-68582 

816 

a  =2  16    4.68  546     4.68  58c 

>   8460  =2  21     4.68545     4.68582 

822 

0  =2  17     4-68  546     4-68  58( 

)   8520  =2  22     4.08  545     4-63  582 

19 


500— 

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5 

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957 

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100 

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120 

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136 

141 

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146 

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156 

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166 

171 

176 

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186 

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202 

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212 

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222 

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247 

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258 

263 

268 

273 

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288 

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359 

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601 

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692 

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9 

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707 

712 

717 

722 

727 

732 

737 

742 

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866 

752 

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762 

767 

772 

777 

782 

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867 

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807 

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847 

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067 

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101 

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874 

151 

156 

161 

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876 

250 

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265 

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877 

300 

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340 

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7 

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349 

354 

359 

364 

369 

374 

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389 

394 

8 

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879 
880 
881 

399 

404 

409 

414 

419 

424 

429 

433 

43S 

443 

9 

4-5 

448 

453 

458 

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46S 

473 

478 

483 

488 

493 

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503 

507 

512 

517 

522 

527 

532 

537 

542 

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547 

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557 

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571 

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586 

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630 

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640 

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650 

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670 

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680 

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694 

699 

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719 

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729 

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763 

768 

773 

778 

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4 

887 

792 

797 

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807 

812 

817 

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832 

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841 

846 

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856 

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866 

871 

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880 

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1 

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910 

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963 

968 

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978 

983 

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*oo7 

*OI2 

*°I7 

*°22 

*°27 

*032 

892 

95036 

041 

046 

051 

056 

061 

066 

071 

075 

080 

7 

2.8 

893 

085 

090 

095 

100 

105 

109 

114 

119 

124 

129 

8 

3-2 

894 

134 

139 

143 

148 

153 

158 

163 

168 

173 

177 

9 

3-6 

895 

182 

187 

192 

197 

202 

207 

211 

216 

221 

226 

896 

231 

236 

240 

245 

250 

255 

260 

265 

270 

274 

897 

279 

284 

289 

294 

299 

303 

308 

313 

3i8 

323 

898 

328 

332 

337 

342 

347 

352 

357 

361 

366 

371 

899 
900 

376 

38i 

386 

390 

395 

400 

405 

410 

415 

419 

424 

429 

434 

439 

444 

448 

453 

45S 

463 

468 

N 

L  0 

1 

2  |  3 

4 

5  |  6  |  7  |  8 

9 

P  P 

8460" 

=  2°  21'    S  4.68  545  T  4.68  582 

8760"  =  2°  26'    S 

4.68  544  T  4.68  5S4 

8520 

=  2  22      4.68  545    4.68  582 

8820  =  2  27 

4.68  544    4-68  584 

8580 

=  2  23      4.68  545    4.68  5S3 

8880   =  2  28 

4.68  544    4-68  584 

8640 

-  2  24      4.68  545    4.68  583 

894O   =  2  29 

4.68  544    4-68  585 

8700 

=  2  25      4.68  545    4.68  583 

9OOO   =  2  30 

4.68  544    4-68  5S5 

20 


900- 

-950 

N  1 

L  0  |  1 

2  |  3 

4 

5  |  6  |  7    8  j  9 

P  P 

900 

95424 

429 

434 

439 

444 

44S 

453 

458 

463 

46S 

901 

472 

477 

4S2 

487 

492 

497 

501 

506 

5ii 

5i6 

902 

521 

525 

530 

535 

540 

545 

550 

554 

559 

b^4 

9°3 

569 

574 

57S 

583 

5S8 

593 

598 

602 

607 

612 

904 

617 

622 

626 

631 

636 

641 

646 

650 

655 

bbo 

905 

665 

670 

674 

679 

684 

689 

O94 

098 

703 

70S 

906 

713 

718 

722 

727 

732 

737 

742 

74b 

751 

75^ 

907 

761 

766 

770 

775 

7S0 

785 

789 

794 

799 

804 

90S 

809 

813 

818 

823 

828 

832 

837 

842 

847 

S52 

909 
910 

911 

856 

861 

866 

871 

875 

880 

885 

890 

895 

899 

904 

909 

914 

918 

923 

928 

933 

938 

942 

947 

995 

952 

Q57 

961 

q66 

971 

976 

980 

985 

990 

912 

999 

,004 

*oo9 

*oi4 

*oi9 

*"23 

,028 

*Q33 

*°38 

*"42 

5 

913 

96047 

052 

057 

061 

06b 

071 

076 

080 

085 

090 

1 

0.5 

9M 

095 

099 

104 

109 

114 

118 

123 

128 

133 

137 

2 

1.0 

9J5 

142 

147 

152 

156 

161 

166 

171 

175 

180 

i»5 

3 

i-5 

916 

190 

194 

199 

204 

209 

213 

218 

223 

227 

232 

4 

2.0 

9*7 

237 

242 

246 

251 

256 

261 

265 

270 

275 

280 

5 

2-5 

918 

284 

289 

294 

298 

303 

308 

313 

317 

322 

32/ 

6 

3-o 

919 
920 

921 

332 

336 

341 

346 

350 

355 

360 

3^5 

3t>9 

3/4 

7 
8 
9 

3-5 
4.0 
4-5 

379 

384 

388 

393' 

398 

402 

407 

412 

417 

421 

426 

431 

435 

440 

445 

450 

454 

459 

464 

468 

922 

473 

478 

483 

487 

492 

497 

501 

506 

511 

515 

923 

520 

525 

530 

534 

539 

544 

548 

553 

558 

562 

924 

567 

572 

577 

581 

586 

59i 

595 

600 

605 

609 

925 

614 

619 

624 

628 

633 

638 

642 

b47 

652 

656 

926 

661 

666 

670 

675 

680 

685 

689 

b94 

b99 

703 

927 

708 

713 

717 

722 

727 

73i 

736 

741 

745 

750 

928 

755 

759 

764 

769 

774 

778 

783 

788 

792 

797 

929 
930 
93i 

802 

806 

811 

816 

820 

825 

830 

834 

839 

844 

4 

848 

853 

858 

862 

867 

872 

876 

881 

886 

890 

89! 

900 

904 

909 

914 

918 

923 

928 

932 

937 

932 

942 

946 

95i 

956 

960 

965 

970 

974 

9V9 

984 

1 

0.4 

933 

988 

993 

997 

#002 

*oo7 

*°" 

*OlO 

*021 

#02b  . 

*ojo 

2 

0.8 

934 

97035 

039 

044 

049 

o53 

058 

063 

067 

072 

077 

3 

1.2 

935 

081 

086 

090 

095 

100 

104 

109 

114 

123 

4 

1.6 

936 

128 

132 

137 

142 

146 

151 

155 

160 

165 

169 

.   5 

2.0 

937 

174 

179 

183 

18S 

192 

197 

202 

206 

211 

216 

6 

2-4 

938 

220 

225 

230 

234 

239 

243 

248 

253 

257 

262 

7 

2.8 

939 
940 
94i 

267 

271 

276 

280 

285 

290 

294 

299 

304 

8 
9 

3.2 
3-6 

313 

3i7 

322 

327 

331 

336 

340 

345 

350 

354 

359 

V>4 

368 

373 

377 

3S2 

387 

391 

396 

400 

942 

405 

410 

4M 

419 

424 

428 

433 

437 

442 

447 

943 

45i 

456 

460 

465 

47" 

474 

479 

483 

488 

493 

944 

497 

502 

506 

511 

516 

520 

525 

529 

534 

539 

945 

543 

548 

552 

557 

562 

566 

57i 

575 

580 

5»b 

946 

589 

594 

598 

603 

607 

612 

bi7 

621 

626 

630 

947 

635 

640 

644 

649 

653 

658 

663 

""7 

672 

67b 

948 

681 

685 

690 

695 

699 

704 

708 

713 

717 

722 

949 
95(1 

727 

73i 

736 

74" 

745 

71  1 

754 

759 

763 
809 

__708 

813 

772 

777 

782 

7S(, 

79' 

79: 

8(  K  . 

804 

N 

L  0   1   2   3  :  4 

5  .  .1    7    8  |  9 

1'  P 

900 
906 
912 

918 

3*  —2°  30'  S   4.68544   T   4.6858; 
0    =2  31     4- 68  544     4-68  58f 
0  —2  32     4.68  543     4-68  58( 

9300'  =2°  35'  S  4.68  543  T  4-68  587 
9360  =2  36     4-68543     4-68587 

MJ"    J  ;7      ' ■'" :542      4-SlSS 

0  =2  -n     4.68  543     4-68  58( 

,,-,,            t .-  -  -»-     4-68  588 
9540   2  39    4-68  543     -i-"s  588 

924 

0  =2  ; 

4 

4.68 

543 

4- 

68  58 

21 


950 

—1000 

N 

L  0 

1 

2 

3 

4 

5  |  6 

7 

8 

9 

P  P 

950 

95i 

97  772 

777 

7S2 

786 

791 

795 

800 

804 

809 

813 

818 

823 

827 

832 

836 

841 

845 

850 

855 

859 

952 

864 

868 

873 

877 

882 

886 

891 

896 

900 

9°  5 

953 

909 

914 

918 

923 

928 

932 

937 

941 

946 

95o 

954 

955 

959 

964 

968 

973 

978 

982 

987 

991 

996 

955 

98000 

005 

009 

014 

019 

023 

028 

032 

037 

041 

956 

046 

050 

055 

059 

064 

068 

073 

078 

082 

087 

957 

091 

096 

100 

105 

109 

114 

118 

123 

127 

132 

958 

137 

141 

146 

150 

155 

159 

164 

168 

173 

177 

959 
960 
961 

182 

186 

191 

i95 

200 

204 

209 

214 

218 

223 

5 

227 

232 

236 

241 

245 

250 

254 

259 

263 

268 

272 

277 

281 

286 

290 

295 

299 

304 

308 

313 

962 

318 

322 

327 

33i 

336 

34o 

345 

349 

354 

358 

1 

0.5 

963 

363 

367 

372 

376 

38i 

385 

390 

394 

399 

4o3 

2 

1.0 

964 

408 

412 

417 

421 

426 

430 

435 

439 

444 

448 

3 

i-5 

965 

453 

457 

462 

466 

47i 

475 

480 

484 

489 

493 

4 

2.0 

966 

498 

502 

507 

5" 

516 

520 

525 

529 

534 

538 

5 

2-5 

967 

543 

547 

552 

556 

561 

565 

570 

574 

579 

583 

6 

3-0 

968 

588 

592 

597 

601 

605 

610 

614 

619 

623 

628 

7 

3-5 

969 

970 
97i 

632 

637 

641 

646 

650 

655 

659 

664 

668 

673 

8 
9 

4.0 
4-5 

677 

682 

686 

691 

695 

700 

704 

709 

713 

717 

722 

726 

731 

735 

740 

744 

749 

753 

758 

762 

972 

767 

771 

776 

780 

784 

789 

793 

798 

802 

807 

973 

811 

816 

820 

825 

829 

834 

838  . 

843 

847 

851 

974 

856 

860 

865 

869 

874 

878 

683 

887 

892 

896 

975 

900 

9°5 

909 

914 

918 

923 

927 

932 

936 

941 

976 

945 

949 

954 

958 

963 

967 

972 

976 

981 

985 

977 

989 

994 

998 

*°°3 

*°°7 

*OI2 

£016 

JJ.02I 

*025 

*02g 

978 

99034 

038 

043 

047 

052 

056 

061 

065 

069 

074 

979 
980 
981 

078 

083 

087 

092 

096 

IOO 

105 

IO9 

114 

118 

4 

123 

127 

131 

136 

140 

145 

149 

154 

158 

162 

167 

171 

176 

180 

185 

189 

193 

I98 

202 

207 

982 

211 

216 

220 

224 

229 

233 

238 

242 

247 

251 

1 

0.4 

983 

255 

260 

264 

269 

273 

277 

282 

286 

291 

295 

2 

0.8 

984 

300 

304 

308 

313 

317 

322 

326 

330 

335 

339 

3 

1.2 

985 

344 

348 

352 

357 

361 

366 

37o 

374 

379 

383 

4 

1.6 

986 

388 

392 

396 

401 

405 

4IO 

414 

419 

423 

427 

5 

2.0 

987 

432 

436 

441 

445 

449 

454 

458 

463 

467 

47i 

6 

2.4 

988 

476 

480 

484 

489 

493 

498 

502 

506 

5ii 

5i5 

7 

2.8 

989 
990 
99r 

520 

524 

528 

533 

537 

542 

546 

550 

555 

559 

8 
9 

3.2 
3-6 

564 

568 

572 

577 

58i 

585 

59° 

594 

599 

603 

607 

612 

616 

621 

625 

629 

634 

638 

642 

647 

992 

651 

656 

660 

664 

669 

673 

677 

682 

686 

691 

993 

695 

699 

704 

708 

712 

717 

721 

726 

730 

734 

994 

739 

743 

747 

752 

756 

760 

765 

769 

774 

778 

995 

782 

787 

791 

795 

800 

804 

808 

813 

817 

822 

996 

826 

830 

8.35 

839 

843 

848 

852 

856 

861 

865 

997 

870 

874 

878 

883 

887 

891 

896 

900 

904 

909 

998 

913 

917 

922 

926 

930 

935 

939 

944 

948 

952 

999 
1000 

957 

961 

965 

970 

974 

978 

983 

9S7 

991 

996 

00000 

004 

009 

013 

"17 

022 

026 

030 

035 

039 

N 

L  0 

1 

2 

3 

4 

5  |  6  |  7 

8  |  9 

P  P 

948c 

*  —  2°  38'  S  4.68542  T  4.68588 

9780"  =2°  43'  S  4.68541  T  4.68590 

954C 

=2  39    4.68  542     4.68  588 

9840  =2  44    4.68  541     4.68  590 

960c 

>  =2  40    4.68542     4.68589 

9900  =2  45    4.68  541     4.68  591 

966c 

=  2  41     4.68  542     4.  68  589 

9960  =2  46    4.68  541     4.68  591 

972c 

>  =2  42    4.68  541     4.68  590 

10020  =2  47    4.68540     4.68592 

THE 

NATURAL    LOGARITHMS 

WHOLE  NUMBERS  FROM  1  TO  200. 

Common  logarithms  may  be  converted  into  natural  logarithms  by  multi- 

plying them  by  2.302585093C 

. 

Natural   logarith 

ms   may 

be    converted 

into    common 

ogarithms    by 

multiplying  them  by  0.4342944819 

N 

Nat  Log 

N 

Nat  Log 

N 

Nat  Log 

N 

Nat  Log 

N 

Nat  Log 

0 

—  oo 

40 
4i 

3.68  888 

80 
81 

4-38  203 

120 

121 

4-78  749 

160 
161 

5-07517 

o.oo  ooo 

3-7i  357 

4-39  445 

4-79  579 

5.08  140 

2 

0.69315 

42 

3-73  767 

82 

4.40  672 

122 

4.80  402 

162 

5.08  760 

3 

1.09  861 

43 

3.76  120 

83 

4.41  884 

123 

4.81  218 

163 

5.09  375 

4 

1.38  629 

44 

3-78  4I9 

84 

4.43  082 

124 

4.82028 

164 

5.09987 

5 

1.60944 

45 

3.80666 

85 

4.44  265 

125 

4.82  831 

165 

5-10595 

6 

1.79 176 

46 

3.82  864 

86 

4-45  435 

126 

4.83  628 

166 

5-.ii  199 

7 

1.94  591 

47 

3.85015 

87 

4.46  591 

127 

4.84419 

167 

5."  799 

8 

2.07  944 

48 

3.87  120 

88 

4-47  734 

128 

4.85  203 

168 

5.12396 

9 
10 

2.19  722 

49 
50 
5i 

3.89182 

89 
90 
91 

4.48  864 

129 
130 
131 

4-85981 

169 
170 
171 

5.12  990 

2.30  259 

3.91  202 

4.49981 

4.86  753 

5-13  580 

2.39  790 

3-93  183 

4.51  086 

4-87  520 

5.14  166 

12 

2.48  491 

52 

3-95  124 

92 

4-52  179 

132 

4.88  280 

172 

5-14  749 

13 

2.56495 

53 

3.97029 

93 

4.53  260 

133 

4-89  035 

i73 

5-I5  329 

14 

2.63  906 

54 

3-98  898 

94 

4-54  329 

134 

4.89  784 

i74 

5-15  906 

15 

2.70  805 

55 

4-oo  733 

95 

4-55  388 

i35 

4.90  527 

i75 

5-I6  479- 

16 

2.77259 

56 

4-02  535 

96 

4-56  435 

136 

4.91  265 

176 

5.17048 

17 

2.83  321 

57 

4-04  305 

97 

4-57  471 

i37 

4.91  998 

i77 

5-17615 

18 

2.89037 

5« 

4.06  044 

98 

4.58497 

138 

4.92  725 

178 

5.18  178 

19 
20 

21 

2.94  444 

59 
60 
61 

4-Q7  754 

99 
100 

IOI 

4-59  512 

139 
140 
141 

.   4-93  447 

179 
180 
181 

5.18739 

2-99  573 

4.09  434 

4-60517 

4.94  164 

5-19296 

3.04452 

4.11087 

4.61  512 

4.94  876 

5-19850 

22 

3-og  104 

62 

4-12713 

102 

4.62  497 

142 

4-95  583 

182 

5.20401 

23 

3-13  549 

63 

4-I43I3 

103 

4-63  473 

i43 

4.96  284 

183 

5.20949 

24 

3-17  805 

64 

4.15  888 

104 

4.64  439 

i44 

4.96981 

184 

5.21  494 

25 

3.21  888 

65 

4-17  439 

105 

4-65  396 

M5 

4-97  673 

185 

5.22  036 

26 

3.25  810 

66 

4-18965 

106 

4.66  344 

146 

4-98  361 

186 

5-22575 

27 

3-29  584 

67 

4.20  469 

107 

4-67  283 

147 

4-99  043 

187 

5-23111 

23 

3.33  220 

68 

4.21951 

108 

4.68  213 

148 

4.99  721 

188 

5.23  644 

29 

30 

3i 

3-3^  730 

69 
70 
7i 

4-23  4U 
4.24850 

109 
110 
in 

4.69  135 

149 
150 

151 

'  5-00395 

189 
190 
191 

5-24I75 

3.40  120 

4.70048 

5.01  064 

5.24  702 

3-43  399 

4.26  268 

4-7»953 

5.01  728 

5.25227 

32 

3-46  574 

72 

4.27  667 

112 

4.71  850 

152 

5.02  388 

192 

5-25  750 

33 

3-49  65 1 

73 

4.29  046 

"3 

4-72  739 

153 

5.03  044 

i93 

5.26  269 

34 

3-52  636 

74 

4.30  407 

114 

4.73  620 

154 

5-03  695 

194 

5.26786 

35 

3-55  535 

75 

4-3 1  749 

"5 

4-74  493 

155 

5-04  343 

195 

5.27300 

36 

3-58  352 

76 

4-33  073 

116 

4-75  359 

156 

5.04  986 

196 

5-27811 

37 

3.61  092 

77 

4-34  38I 

"7 

4.76217 

i57 

5-05  625 

■ '  >  T 

5.28  320 

38 

3-03  759 

78 

4-35  67I 

118 

4.77068 

158 

5.06  260 

198 

5-28827 

39 
40 

3.66356 

79 
80 

4.36945 
4.38  203 

119 

120 

4.77912 

i59 
160 

5.06  890 

199 
200 

5.2.1330 

3.6S  sss 

17-  749 

5.07  5I7 

5-29  832 

23 


II 

TABLE  OF  ADDITION   AND  SUBTRACTION 
LOGARITHMS 


CALCULATION  OF  THE  LOGARITHMS 

OF  THE 

SUM  AND  DIFFERENCE  OF  TWO  NUMBERS  WHOSE 

LOGARITHMS  ARE  GIVEN.  «. 


24 


ADDITION. 

A 

B  0 

> 

2  |  3 

4 

5 

6 

7  |  8 

9 

P  J' 

0.00 

OI 

0.30  103 

053 

003 

*953 

*9°3 

*854 

*8o4 

*754 

*705 

*e>55 

0.29  606 

556 

507 

458 

409 

359 

310 

261 

212 

163 

50 

49 

48 

47 

02 

115 

066 

017 

,,j(,S 

*920 

*«7i 

4.822 

*774 

*726 

*677 

1 

5-o 

4-9 

4.8 

4-7 

03 

0.28629 

581 

532 

484 

436 

388 

340 

292 

245 

197 

2 

1 0.0 

9.8 

9.6 

9-4 

04 

149 

IOI 

054 

006 

*959 

*9" 

*864 

*8i7 

*7&9 

*722 

3 

15.0 

14-7 

14.4 

14.1 

05 

0.27675 

628 

581 

534 

487 

440 

393 

346 

300 

253 

4 

20.0 

19.6 

19.2 

18.S 

06 

207 

160 

114 

067 

021 

*974 

*928 

*882 

*836 

*79° 

5 

25.0 

24-5 

24.0 

2S.8 
33.6 

38.4 

43.2 

23-5 
28.2 
32.9 
37-6 
42.3 

07 

08 

0.26  744 

287 

698 
242 

652 
196 

606 
151 

560 
106 

515 
061 

469 
016 

423 
*97Q 

378 
*926 

332 

*88i 

7 
8 
9 

30.0 
35-o 
40.0 

45.0 

29.4 
34-3 
39-2 
44.1 

09 

0.10 

II 

0.25  836 

791 

746 

701 

657 

612 

568 

523 

479 

434 

390 

346 

302 

258 

214 

170 

126 

082 

038 

*994 

0.24950 

907 

863 

819 

776 

733 

689 

646 

603 

559 

46 

45 

44 

43 

12 

5i6 

473 

43o 

387 

344 

301 

258 

216 

173 

130 

1 

4-6 

4-5 

4-4 

4-3 

13 

088 

045 

003 

*96° 

*9i8 

*875 

*833 

*79i 

*749 

*7Q7 

2 

9.2 

9.0 

8.8 

8.6 

14 

0.23665 

623 

581 

539 

497 

455 

414 

372 

330 

28q 

3 

13.8 
18.4 

13.5 

18.0 

13.2 
17.6 

12.9 

15 

247 

206 

165 

123 

082 

041 

000 

*959 

*9i8 

*877 

4 

16 

17 

0.22  836 
430 

795 
389 

754 
349 

713 
309 

673 
269 

632 
229 

59i 
189 

551 
149 

5io 
109 

470 
069 

b 
6 

- 

27.6 
32.2 

22.5 
27.0 
31.5 

26.4 

30,8 

21.5 
25.8 
30.1 

18 

029 

*9«9 

*949 

*910 

#870 

*83i 

*79* 

*752 

*7I2 

*t>73 

fl 

368 

36.0 

35.2 

34.4 

19 

0.20 
21 

0.21  634 

595 

556 

516 

477 

438 

399 

361 

322 

283 

9 

41.4 

40.5 

3Q.6 

33.7 

244 

206 

167 

128 

090 

052 

013 

*975 

*937 

*S98 

0.20  860 

822 

784 

746 

708 

670 

632 

594 

557 

5iQ 

42 

41 

40 

39 

22 

481 

444 

406 

369 

33i 

294 

2S7 

220 

182 

145 

1 

4.2 

4.1 

4.0 

3-9 

23 

108 

071 

034 

*997 

#960 

*923 

*887 

*85Q 

*8i3 

*777 

2 

8.4 

8.2 

8.0 

7-8 

24 

0.19  740 

704 

667 

631 

595 

558 

522 

486 

450 

414 

4 

12.6 

i6.3 

12.3 
16.4 

12.0 

16.0 

n. 7 
15.6 

25 

378 

342 

306 

270 

234 

198 

163 

127 

091 

056 

26 
27 

020 
0.18668 

*985 
633 

*949 
599 

*9H 
564 

*879 
529 

*844 
494 

*8o8 
460 

*773 
425 

*738 
390 

*703 
356 

ii 

25.2 
29.4 

24.6 

?87 

24.0 
28.0 

19-5 

23-4 
27.3 

28 

322 

287 

253 

218 

1 84 

150 

116 

082 

048 

014 

- 

33-6 

3?,8 

32.0 

31.2 

29 
0.30 

31 

0.17980 

946 

912 

878 

845 

811 

777 

744 

710 

677 

9 

37-8 

36.9 

36.0 

35-1 

643 

610 

577 

544 

5io 

477 

444 

411 

378 

345 

312 

279 

247 

214 

181 

148 

116 

083 

051 

01S 

38 

37 

36 

35 

32 

0.16986 

954 

921 

889 

857 

825 

793 

76i 

729 

6q7 

1 

3-0 
7-6 

3-7 

3-6 

3-5 

33 

665 

633 

601 

56q 

538 

506 

474 

443 

411 

380 

/•4 

J.2 

7.0 

34 

35 

349 
037 

317 
007 

286 
*976 

255 
*945 

224 
*9i4 

192 

*S84 

161 

*853 

130 

*§22 

099 

*792 

068 

*7&i 

•i 

4 
5 
6 

11.4 

15-2 

19.0 
22.8 

n. 1 
14.8 
18.5 
22.2 

IO.8 
I4.4 

10.5 
14.0 
17.5 
21.0 

3*> 

0.15  731 

701 

670 

640 

610 

580 

550 

520 

489 

460 

21  6 

37 

430 

400 

37o 

340 

310 

281 

251 

221 

192 

162 

7 

26.6 

25-9 

25.2 

24.5 

3* 

133 

104 

074 

045 

016 

*986 

*957 

*928 

*8Q9 

^870 

8 

30.4 

29.6 

28.8 

2S.0 

39 
0.40 

41 

0.14  841 

812 

783 

755 

726 

697 

668 

640 

611 

583 

9 

34.2 

33-3 

32.4 

3i.5 

554 

526 

497 

469 

441 

412 

384 

356 

328 

300 

272 

244 

216 

188 

160 

132 

104 

077 

049 

021 

34 

33 

32 

31 

42 

0.13  994 

966 

939 

911 

884 

857 

829 

S02 

775 

74S 

1 

3-4 

3-3 

3.2 

3-i 

43 

721 

<»94 

667 

640 

613 

586 

559 

532 

5o5 

479 

- 

6.8 

6.6 

6.4 

6.2 

44 

452 

425 

399 

372 

346 

319 

293 

267 

240 

214 

i 

10.2 

9.9 

9.6 

9-3 

45 

188 

162 

136 

no 

084 

058 

032 

006 

*98o 

*954 

! 

13.6 

1  J.2 

12.S 

12.4 

40 

0.12928 

903 

877 

851 

826 

800 

77S 

749 

724 

h.,S 

- 

17.0 

16.5 

16.0 

i5-5 

47 

673 

648 

622 

597 

572 

547 

522 

497 

472 

447 

b 

20.4 

27.2 
10.6 

I9.8 
23.I 
26.4 

20. 7 

19.2 
22.4 
25.6 
28.8 

i8.() 

48 

422 

397 

372 

348 

323 

298 

2  74 

249 

224 

200 

fl 

24.S 
27.0 

49 
0.50 

175 

'  S  " 

127 

102 

078 

"S| 

030 

005 

:;I|M 

#957 

9 

0.1  1  .,33 

,,,„, 

885 

8(.i 

837 

814 

790 

766 

742 

719 

A 

B  0  |  1 

2  |  3 

4 

5  |  6  j  7  |  8  |  9 

1'  P 

a 

>/>, 

A  =  log  a  —  log  b,         log  ( a  +  b  )  =  log  a  +  B. 

ADDITION. 

A 

B  0  |  1 

2 

3 

4 

5 

6 

7 

8 

9 

P  P 

0.50 
5i 

0.11  933 

909 

885 

861 

837 

814 

790 

766 

742 

7i9 

695 

671 

648 

624 

601 

577 

554 

53i 

507 

484 

x 

3-0 

6.0 

2.9 

5-8 
8.7 

so 

2.8 

2.7 
5.4 

52 

46! 

438 

415 

392 

368 

345 

323 

300 

277 

254 

2 

5.6 

8.4 

53 

231 

208 

186 

163 

140 

118 

095 

073 

050 

028 

3 

9.0 

8.1 

54 

005 

*983 

45.960 

*938 

*9l6 

*S94 

*872 

*849 

*827 

*8o5 

4 

12.0 

11.6 

II. 2 

10.8 

55 

0.10  783 

761 

739 

718 

696 

674 

652 

630 

609 

587 

; 

15.0 

M-5 

I4.O 

13-5 

56 

565 

544 

522 

5oi 

479 

458 

437 

4i5 

394 

373 

6 

18.0 

17-4 

16.8 

16.2 

57 

351 

330 

309 

288 

267 

246 

225 

204 

183 

162 

7 

21.0 

20.3 

I9.6 

18.9 

58 

141 

120 

100 

079 

058 

038 

017 

*996 

*976 

*955 

8 

24.0 

23.2 

22.4 

21.6 

59 

0.60 

61 

0.09  935 

914 

894 

874 

853 

833 

813 

793 

773 

752 

9 

27.0 

26.1 

25.2 

24-3 

732 

712 

692 

672 

652 

632 

612 

593 

573 

553 

533 

514 

494 

474 

455 

435 

416 

396 

377 

357 

26 

2.6 

Zb 

24 

223 

62 

338 

319 

299 

280 

261 

242 

223 

204 

184 

165 

1 

2-5 

2.4 

4.8 

7-2 

9.6 

2-3 

4.6 
6.9 
9.2 

63 

146 

127 

108 

090 

071 

052 

033 

014 

*996 

*977 

3 

4 

5-2 

7.8 

10.4 

5-o 

7-5 

10.0 

64 

0.08  958 

940 

921 

902 

884 

865 

847 

829 

810 

792 

65 

774 

755 

737 

719 

701 

683 

664 

646 

628 

610 

5 

13.0 

12.5 

12.0 

n-5 

66 

592 

574 

557 

539 

521 

503 

485 

468 

450 

432 

6 

15.6 

15.0 

14.4 

13-8 

67 

415 

397 

379 

362 

344 

327 

309 

292 

275 

257 

7 

18.2 

17-5 

16.8 

16.1 

68 

240 

223 

206 

188 

171 

154 

137 

120 

103 

086 

- 

20.8 

20.0 

19.2 

18.4 

69 
0.70 

7i 

069 

052 

035 

018 

001 

*9S5 

*968 

*95i 

*934 

*9i8 

9 

234 

22.5 

21.6 

20.7 

0.07  901 

884 

868 

851 

835 

818 

802 

785 

769 

753 

736 

720 

704 

687 

671 

655 

639 

623 

607 

591 

22 

21 

19 

18 

72 

575 

559 

543 

527 

5ii 

495 

479 

463 

448 

432 

1 

2.2 

2.1 

1.9 

1.8 

73 

416 

400 

385 

369 

354 

338 

322 

307 

291 

276 

2 

4.4 
6.6 

8.8 

4.2 

6.3 

8.4 

10.5 

12.6 

3-8 
5-7 
7.6 
9-5 
1 1.4 

3-6 

5-4 
7.2 

74 

261 

24  5 

230 

215 

199 

184 

169 

154 

138 

123 

3 

4 
5 
6 

75 

108 

093 

078 

063 

048 

033 

018 

003 

^988 

*973 

1 1.0 

9.0 
10.8 

76 

0.06  959 

944 

929 

914 

900 

885 

870 

856 

'841 

827 

13.2 

77 

812 

798 

783 

769 

754 

740 

725 

711 

697 

683 

7 

15-4 

14.7 

13-3 

12.6 

78 

668 

654 

640 

626 

612 

597 

583 

569 

555 

541 

8 

17.6 

16.8 

15-2 

M-4 

79 
0.80 

527 

513 

500 

486 

472 

458 

444 

43o 

417 

403 

9 

19.8 

18.9 

17.1 

16.2 

389 

376 

362 

348 

335 

321 

308 

294 

281 

267 

81 

254 

240 

227 

214 

200 

187 

174 

161 

147 

134 

17 

16 

1.6 

15 

14 

82 

121 

108 

09! 

082 

069 

056 

043 

030 

017 

004 

1 

w 

!-5 

1-4 

2.8 

4.2 

5-6 

83 

0.05  991 

978 

965 

952 

939 

927 

914 

901 

889 

876 

3 

4 

3-4 
5-i 
6.8 

3- 

4.8 

6.4 

3-° 
4-5 
6.0 

84 

863 

851 

838 

825 

813 

800 

788 

775 

763 

75i 

85 

738 

726 

714 

701 

689 

677 

664 

652 

640 

628 

5 

8-5 

8.0 

7-5 

7.0 

86 

616 

604 

591 

579 

567 

555 

543 

53i 

519 

508 

6 

10.2 

9.6 

9.0 

8.4 

87 

496 

484 

472 

460 

448 

436 

425 

413 

401 

390 

7 

11.9 

II. 2 

10.5 

9.8 

88 

378 

366 

355 

343 

332 

320 

308 

297 

286 

274 

8 

13-6 

12.8 

12.0 

n. 2 

89 
0.90 

9i 

263 

251 

240 

229 

217 

206 

195 

183 

172 

161 

9 

15-3 

14.4 

13-5 

12.6 

150 

139 

127 

116 

105 

094 

083 

072 

061 

050 

039 

028 

017 

006 

*995 

*9S! 

*974 

*9&3 

*952 

*94i 

13 

12 

11 

9 

92 

0.04931 

920 

909 

898 

888 

877 

867 

856 

845 

835 

i 

i-3 

2.6 

3-9 

5.2 

1.2 

1.1 

0.9 
1.8 
2.7 
3.6 

93 

824 

814 

803 

793 

7S2 

772 

762 

75i 

74i 

731 

2 

2.4 
3.6 
4.8 

2.2 

3-3 
4.4 

94 

720 

710 

700 

689 

679 

669 

659 

649 

639 

628 

3 

4 

95 

618 

608 

598 

588 

578 

568 

558 

54S 

538 

528 

s 

6.5 

6.0 

5-5 

4-5 

96 

519 

509 

499 

489 

479 

469 

460 

45o 

440 

430 

6 

7.8 

7-2 

6.6 

5-4 

97 

421 

411 

401 

392 

382 

373 

363 

353 

344 

334 

7 

9.1 

8.4 

7-7 

6.3 

98 

325 

315 

306 

297 

287 

278 

268 

259 

250 

240 

- 

10.4 

9.6 

8.8 

7-2 

99 
1.00 

231 

222 

213 

203 

194 

185 

176 

167 

157 

148 

9 

11. 7 

10.8 

9.9 

8.1 

139 

130 

121 

112 

103 

094 

085 

076 

067 

058 

A 

B  0 

1 

2 

3 

4 

5  |  6 

7 

8 

9 

P  P 

a>b, 

A  =  log  a  — 

log  b, 

log  (a  + 

b )  =  log  a  +  B. 

ADDITION. 

A 

B  0 

1 

2 

3 

4 

5    6 

7 

8    9 

P  P 

1.00 

OI 

0.04  139 

130 

121 

112 

103 

094 

085 

07b 

ob7 

058 

9 

049 

040 

032 

023 

014 

005 

*996 

*987 

*979 

*97Q 

02 

0.03  961 

953 

944 

935 

926 

918 

909 

901 

892 

883 

1 

0.9 

03 

875 

86b 

858 

849 

841 

832 

824 

816 

807 

799 

04 

790 

782 

774 

765 

757 

749 

74i 

732 

724 

716 

3 
4 
5 
b 

2-7 

3-6 

4-5 
5.4 

05 

708 

700 

691 

683 

675 

667 

659 

6fii 

643 

635 

06 

627 

big 

611 

603 

595 

587 

579 

57i 

563 

555 

°7 

548 

540 

532 

524 

5i6 

509 

501 

493 

485 

47S 

7 

6-3 

08 

470 

4b2 

455 

447 

439 

432 

424 

417 

409 

401 

8 

7.2 

09 
1.10 

394 

38b 

379 

371 

3t>4 

357 

349 

342 

334 

327 

9 

8.1 

320 

312 

305 

298 

290 

283 

27b 

2b8 

261 

254 

247 

240 

232 

225 

218 

211 

204 

197 

190 

183 

8 

7 

12 

175 

ib8 

ibi 

154 

M7 

140 

133 

12b 

120 

"3 

1 

0.8 

0.7 

13 

106 

099 

092 

085 

078 

071 

065 

058 

051 

044 

2 

i.b 

1.4 

14 

o37 

031 

024 

017 

on 

004 

*997 

*99l 

*984 

*977 

3 

2.4 

2.8 

15 

0.02  971 

964 

957 

951 

944 

938 

931 

925 

918 

912 

3-2 

16 

905 

899 

892 

88b 

879 

873 

8b7 

Sbo 

854 

848 

5 

4.0 

4.8 

5  6 

3-5 

17 

841 

S35- 

829 

822 

816 

810 

803 

797 

791 

785 

4.8 

18 

779 

772 

7bb 

7bo 

754 

748 

742 

735 

729 

723 

8 

ft  1 

5-6 

19 
1.20 

21 

717 

711 

705 

b99 

693 

bS7 

6b  1 

675 

669 

6b3 

9 

7.2 

6-3 

657 

651 

645 

639 

634 

b28 

b22 

bib 

bio 

604 

6 

599 

593 

587 

58i 

575 

570 

564 

558 

552 

547 

22 

54i 

535 

530 

524 

518 

513 

507 

502 

496 

490 

1 

o.b 

23 

485 

479 

474 

4b8 

4^3 

457 

452 

446 

441 

435 

2 

1.2 

24 

430 

424 

419 

414 

408 

403 

397 

392 

387 

3Si 

3 

1.8 

25 

376 

371 

365 

3  bo 

355 

350 

344 

3*39 

334 

329 

4 

2.4 

26 

323 

3i8 

313 

308 

303 

297 

292 

287 

282 

277 

5 
6 
7 

3-o 
3-6 
4.2 

4.8 
5-4 

27 

272 

267 

2b2 

257 

252 

24b 

241 

236 

231 

22b 

28 

221 

216 

211 

207 

202 

197 

192 

187 

182 

177 

29 
1.30 

31 

172 

ib7 

162 

158 

153 

148 

M3 

138 

133 

129 

9 

124 

119 

114 

no 

105 

100 

095 

091 

08b 

081 

077 

072 

ob7 

ob3 

058 

053 

049 

044 

040 

035 

5 

4 

32 

030 

02b 

021 

017 

012 

008 

003 

*999 

*994 

*99° 

1 

0.5 

0.4 

33 

0.01  985 

981 

97b 

972 

967 

9£>3 

959 

954 

950 

945 

2 

1.0 

0.8 

34 

941 

937 

932 

928 

924 

919 

915 

911 

906 

902 

3 

1.5 

1.2 

35 

898 

894 

889 

88s 

8S1 

877 

872 

868 

8b,] 

860 

4 

2.0 

i.b 

30 

856 

«5i 

847 

843 

839 

835 

831 

827 

822 

818 

5 

2-5 

2.0 

37 

814 

810 

80b 

802 

798 

794 

790 

786 

7S2 

778 

b 

3-o 

2.4 
2.8 

38 

774 

770 

7bb 

7b2 

758 

754 

75o 

746 

742 

738 

7 
8 

3-5 

39 
1.40 

41 

734 

730 

72b 

722 

7i9 

715 

7" 

707 

703 

699 

40 

3-2 

n.6 

695 

bg2 

b88 

b84 

bSo 

b76 

673 

bbg 

665 

661 

R 

658 

654 

650 

b4b 

643 

639 

635 

632 

628 

b24 

42 

621 

617 

613 

bio 

bob 

002 

599 

595 

591 

58S 

1 

0.3 

43 

584 

58i 

577 

574 

570 

56b 

5^3 

559 

556 

552 

2 

o.b 

44 

549 

545 

542 

538 

535 

531 

528 

525 

521 

5i8 

3 

0.9 

45 

5M 

5" 

507 

504 

501 

497 

494 

490 

487 

484 

4 

1.2 

46 

480 

477 

474 

470 

467 

464 

4bo 

457 

454 

450 

5 

i-5 

47 

447 

444 

441 

437 

434 

43i 

428 

424 

421 

418 

6 

1.8 

48 

415 

412 

408 

405 

402 

399 

396 

393 

389 

38b 

7 

2.1 

49 
1.50 

383 

380 

377 

374 

371 

368 

364 

361 

358 

.;;; 

8 
9 

2.4 

2-7 

).oi  352 

U<) 

346 

i  l  ■■• 

340 

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334 

33* 

328 

325 

A 

B  0  |  1 

2 

3  |  4 

5  1  6  |  7  1  8  1  I. 

P   P 

a  >  b,         A  —  log  a  —  log  b,         log  (  a  +  /> )  =  log  a  +  f*. 

2V 


ADDITION. 

A 

1$  0 

1 

2 

3 

4 

5 

6 

7 

8 

') 

P  P 

1.50 
5' 

0.01  352 

349 

346 

343 

34o 

337 

334 

33i 

328 

325 

322 

319 

316 

313 

310 

307 

304 

301 

298 

295 

52 

292 

289 

286 

283 

280 

278 

275 

272 

269 

266 

53 

263 

260 

257 

255 

252 

249 

246 

243 

240 

238 

54 

235 

232 

229 

226 

224 

221 

218 

215 

213 

210 

55 

207 

204 

202 

199 

196 

193 

191 

188 

185 

183 

•56 

180 

177 

i75 

172 

169 

167 

164 

161 

159 

156 

57 

153 

151 

148 

146 

143 

140 

138 

i35 

i33 

130 

58 

128 

125 

122 

120 

"7 

115 

112 

no 

107 

105 

59 

1.60 

61 

102 

100 

097 

095 

092 

090 

087 

085 

082 

080 

0.01  077 

07! 

073 

070 

068 

065 

063 

060 

058 

056 

053 

051 

048 

046 

044 

041 

039 

037 

034 

032 

62 

030 

027 

025 

022 

020 

018 

016 

013 

on 

009 

63 

006 

004 

002 

*999 

*997 

*995 

*993 

*99<> 

*988 

*98(j 

64 

0.00  984 

981 

979 

977 

975 

973 

970 

968 

966 

964 

65 

962 

959 

957 

955 

953 

951 

948 

946 

944 

942 

66 

940 

938 

936 

933 

93i 

929 

927 

925 

923 

921 

67 

919 

917 

915 

912 

910 

908 

906 

904 

902 

900 

2 

68 

898 

896 

894 

892 

890 

888 

886 

884 

882 

880 

I 

0.3 
0.6 
0.9 
1.2 
1-5 

69 
1.70 

7i 

878 

876 

874 

872 

870 

868 

866 

864 

862 

860 

2 

3 
4 
5 

0.00  858 

856 

854 

852 

850 

848 

846 

844 

842 

841 

839 

837 

835 

833 

831 

829 

827 

825 

823 

822 

72 

820 

818 

816 

814 

812 

810 

809 

807 

805 

803 

6 

1.8 

73 

801 

799 

798 

796 

794 

792 

790 

789 

787 

785 

7 

2.1 

74 

783 

781 

780 

778 

776 

774 

773 

77i 

769 

767 

8 

2.4 

75 

766 

764 

762 

760 

759 

757 

755 

753 

752 

750 

9 

2*7 

76 

748 

747 

745 

743 

741 

740 

738 

736 

735 

733 

77 

731 

730 

728 

726 

725 

723 

721 

720 

718 

716 

78 

715 

713 

712 

710 

708 

707 

705 

703 

702 

700 

79 

1.80 

81 

699 

697 

696 

694 

692 

691 

689 

688 

686 

684 

0.00  683 

681 

680 

678 

677 

675 

674 

672 

671 

669 

667 

666 

664 

663 

661 

660 

658 

657 

655 

654 

82 

652 

651 

649 

648 

646 

645 

644 

642 

641 

639 

83 

638 

636 

635 

633 

632 

630 

629 

628 

626 

625 

84 

623 

622 

620 

619 

618 

616 

615 

613 

612 

611 

85 

609 

608 

606 

605 

604 

602 

601 

599 

598 

597 

86 

595 

594 

593 

591 

59° 

589 

587 

586 

585 

583 

87 

582 

58i 

579 

578 

577 

575 

574 

573 

571 

570 

88 

569 

567 

566 

565 

564 

562 

56i 

560 

558 

557 

89 
1.90 

91 

556 

555 

553 

552 

55i 

550 

548 

547 

546 

545 

0.00  543 

542 

541 

540 

538 

537 

536 

535 

533 

532 

53i 

530 

529 

527 

526 

525 

524 

523 

52i 

520 

92 

519 

5i8 

517 

515 

5i4 

513 

512 

511 

5io 

508 

93 

507 

506 

505 

504 

503 

502 

500 

499 

498 

497 

94 

496 

495 

494 

492 

491 

490 

489 

48S 

487 

486 

95 

485 

483 

482 

481 

480 

479 

478 

477 

476 

475 

96 

474 

473 

471 

470 

469 

468 

467 

466 

465 

464 

97 

463 

462 

461 

460 

459 

458 

457 

456 

454 

453 

98 

452 

45i 

450 

449 

448 

447 

446 

445 

444 

443 

99 
2.00 

442 

441 

440 

439 

438 

437 

436 

435 

434 

433 

0.00  432 

43i 

430 

429 

428 

427 

426 

425 

424 

423 

A 

B  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P  P 

cO 

>  b,          A—\oga  —  log  b,          log  (a-\-  b)  =  loga-f-_R 

ADDITION. 

A 

J3    0 

1 

2 

3 

4 

5    |    6 

' 

* 

9 

P    P 

2.0 

o.oo  432 

422 

413 

403 

394 

3S5  1  377 

368 

360 

352 

9 

8 
0.8 

344 

336 

328 

321 

313 

306 

299 

293 

286 

2S0 

1 

0.9 

2 

273 

267 

261 

255 

249 

244 

23S 

233 

227 

222 

1.8 

1.6 

3 

217 

212 

207 

203 

198 

194 

189 

185 

181 

177 

3 

2.7 

3-6 
4-5 
5-4 
6.3 
7.2 

2.4 

4 

173 

169 

165 

I6l 

157 

154 

150 

147 

144 

140 

4 
5 
6 

3-2 

4.0 

4-8 
5-6 
6.4 

7.2 

5 

137 

134 

131 

128 

125 

122 

119 

117 

114 

in 

6 

109 

106 

104 

102 

099 

097 

095 

093 

091 

089 

7 

087 

085 

083 

0S1 

079 

077 

075 

074 

072 

070 

8 

S 

069 

067 

066 

064 

063 

061 

060 

059 

057 

056 

9 

8.T 

9 
3.0 

055 

053 

052 

051 

050 

049 

048 

047 

045 

044 

0.00  043 

042 

041 

041 

040 

039 

038 

037 

036 

035 

_ 

6 

5 

0.5 

i 

034 

034 

033 

032 

031 

031 

030 

029 

029 

02S 

I 

0.7 

0.6 

2 

027 

027 

026 

026 

025 

024 

024 

023 

023 

022 

2 

1-4 

1.2 

1.0 

3 

022 

021 

021 

020 

020 

019 

019 

019 

018 

018 

3 

2.1 

1.8 

i-5 

4 

017 

017 

017 

016 

016 

015 

015 

015 

014 

014 

4 

2.8 

2.4 

2.0 

5 

014 

013 

013 

013 

013 

012 

012 

012 

on 

on 

5 

3-5 

3-o 

2-5 

6 

on 

on 

010 

010 

010 

010 

010 

009 

009 

009 

6 

4.2 

3-0 

3-o 

7 

009 

008 

008 

008 

008 

008 

008 

007 

007 

007 

7 
8 
9 

4.9 
5-6 
6-3 

4.2 

4.8 
5-4 

3-5 

8 

9 

4.0 

007 
005 

007 

005 

007 

005 

006 

005 

006 
005 

006 
005 

006 
005 

006 
005 

006 
005 

006 
004 

4.0 

4-5 

0.00  004 

004 

004 

004 

004 

004 

004 

004 

004 

004 

4 

a 

i 

003 

003 

003 

003 

003 

003 

003 

003 

003 

003 

0.4 
08 

0.3 
0.6 

2 

003 

003 

003 

003 

002 

002 

002 

002 

002 

002 

3 

002 

002 

002 

002 

002 

002 

002 

002 

002 

002 

3 

T.2 

0.9 

4 

002 

002 

002 

002 

002 

002 

002 

OOI 

OOI 

OOI 

4 

1.6 

1.2 

5 

001 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

5 

2.0 

1.5 

b 

001 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

6 

2.4 

1.8 

7 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

7 

2.8 

2.1 

8 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

8 

3-2 

2.4 

9 
5.0 

OOI 

OOI 

OOI 

OOI 

OOO 

OOO 

OOO 

OOO 

OOO 

000 

9 

3-b 

2-7 

0.00000 

000 

OOO 

OOO 

OOO 

OOO 

OOO       OOO 

OOO 

OOO 

A 

B    0 

1 

2 

3 

4 

5 

6     1     7 

8 

9 

P     P 

a>l 

A  =  k>£ 

ra  — 

log  b,            log 

(a  4 

•&)  = 

log  a  +  B. 

The  abo 

ve  ta 

ble  of  Adc 
log  (a 

lition 

Logarithms  is 
=  kgo(l  +  i 

=  loga  +  log( 

base 

-) 

1  + 

d  on 

l) 

the  identity 

The  arg 

umen 

t  A  is  log 

a 
b>* 

nd  the  function 

B  i 

3  log 

/i+A\ 

0     .  conse- 

quently 

1 

Og(tt 

+  6)  =  loga  + 

B. 

29 


SUBTRACTION. 

A 

U  0 

1 

2 

3  |  4 

5  |  6 

1 

8 

9 

P  p 

0.300  [ 
301 

>.30  206 

196 

1S6 

176 

166 

15''  146 
056  046 

136 

126 

116 

016 

106 

096 

086 

076 

066 

036 

026 

302 

006  ^ 

.996  ., 

.9S6  , 

.976  , 

966  j 

956  * 

947  4 

-937  « 

927  *9r7 

303  c 

).2g  907 

897 

887 

877 

867 

857  • 

S48 

S38 

828 

818 

304 

808 

798 

788 

778 

769 

759 

749 

739 

729 

719 

305 

710 

700 

690 

680 

670 

661 

651 

641 

631 

621 

306 

612 

602 

592 

582 

573 

5<>3 

553 

543 

534 

524 

307 

514 

504 

495 

485 

475 

465 

456 

446 

436 

427 

308 

417 

407 

398 

388 

378 

3<>9 

359 

349 

340 

33o 

309 
0.310 

3" 

320 

311 

30I 

291 

282 

272 

263 

253 

243 

234 

224 

215 

205 

195 

186 

176 

167 

157 

M7 

138 

128 

119 

109 

100 

090 

081 

071 

062 

052 

043 

312 

033 

024 

014 

005 

*995 

*9«b 

t97b 

*9<>7 

*957 

*948 

9 

3i3 

3.28938 

929 

919 

910 

900 

891 

881 

872 

862 

853 

1 

0.9 

3M 

S44 

S34 

82S 

815 

806 

797 

787 

778 

768 

759 

2 

1.8 

3i5 

750 

740 

731 

721 

712 

703 

693 

684 

675 

665 

3 

2-7 

316 

656 

647 

637 

628 

619 

609 

600 

59i 

58i 

572 

4 

3-6 

3i7 

563 

553 

S44 

535 

52  5 

516 

507 

498 

488 

479 

5 

4-5 

318 

470 

461 

451 

442 

433 

424 

414 

405 

39t> 

387 

6 

5-4 

319 
0.320 

321 

377 

368 

359 

350 

341 

331 

322 

3'3 

304 

295 

7 
8 
9 

6-3 
7-2 

8.1 

285 

276 

267 

258 

249 

240 

230 

221 

212 

203 

194 

185 

176 

166 

157 

148 

139 

130 

121 

112 

322 

103 

094 

084 

075 

066 

057 

048 

039 

030 

021 

323 

012 

003 

*994 

*985 

*97& 

*9*>7 

*95« 

*94b 

*939 

*930 

324 

0.27921 

912 

903 

894 

885 

876 

867 

858 

849 

840 

325 

831 

822 

813 

804 

796 

787 

778 

769 

760 

75i 

326 

742 

733 

724 

715 

706 

697 

688 

679 

670 

661 

327 

653 

644 

635 

626 

617 

608 

599 

590 

58i 

573 

328 

564 

555 

546 

537 

528 

5i9 

5'i 

502 

493 

484 

329 
0.330 

33i 

475 

466 

458 

449 

440 

43i 

422 

414 

405 

39^ 

8 

387 

378 

370 

361 

352 

343 

335 

326 

317 

308 
221 

300 

291 

282 

273 

265 

256 

247 

238 

230 

332 

212 

204 

IPS 

186 

177 

169 

160 

151 

143 

134 

1 

0.8 

333 

125 

117 

108 

099 

091 

082 

073 

065 

056 

047 

2 

1.6 

334 

039 

030 

021 

013 

004 

*99& 

*987 

*978 

*97o 

^961 

3 

2.4 

335 

0.26953 

944 

935 

927 

918 

910 

901 

892 

884 

875 

4 

3-2 

336 

867 

858 

850 

841 

832 

824 

815 

807 

798 

790 

5 

4.0 

337 

781 

773 

764 

756 

747 

739 

730 

722 

713 

705 

6 

4.8 

338 

696 

688 

679 

671 

662 

654 

645 

637 

62b 

620 

7 

5-6 

339 
0.340 

34i 

611 

603 

595 

586 

578 

5^9 

56i 

552 

544 

535 

8 
9 

6.4 
7-2 

527 

519 

5io 

502 

493 

485 

477 

468 

460 

45i 

443 

435 

426 

418 

410 

401 

393 

3S4 

376 

368 

342 

359 

351 

343 

334 

326 

3i8 

309 

301 

293 

284 

343 

276 

268 

259 

251 

243 

235 

226 

218 

210 

201 

344 

193 

185 

177 

168 

160 

152 

M4 

135 

127 

119 

345 

in 

102 

094 

086 

078 

069 

061 

053 

045 

036 

346 

028 

020 

012 

004 

*995 

*987 

*979 

*97i 

*9^3 

*955 

347 

0.25  946 

938 

930 

922 

914 

906 

897 

889 

881 

873 

34S 

865 

857 

849 

840 

832 

824 

816 

808 

800 

792 

34') 
0.350 

784 

775 

767 

759 

75i 

743 

735 

727 

719 

7ii 

0.25  703  |  695 

687 

678 

670 

(,t,2 

654 

646 

638 

1  630 

A 

BO  |  1 

2  |  3 

4 

5  |  6  |  7  |  8  |  9 

P  P 

a  >  b.        Put  x  =  log  a  —  log  6. 

Ifa;>.3,   then   x  =  A        and   log  (a  —  b)  =  log  a  —  B. 

If  x  <  .3,   then   x  =  B       and   log  (a— b)  =  \oga—A. 

30 


SUBTRACTION. 

A 

IS  (i 

1 

-    ;< 

4 

5 

6 

7 

8 

it 

P  P 

0.350 
35i 

0.25  703 

..„? 

6S7 

678 

.670 

662 

654 

646 

'..;- 

630 

622 

614 

606 

598 

59° 

582 

574 

566 

558 

550 

352 

542 

534 

^26 

518 

5io 

502 

494 

4S6 

478 

470 

353 

462 

454 

446 

438 

430 

422 

4M 

406 

398 

390 

354 

382 

374 

367 

359 

35i 

343 

335 

327 

3i9 

311 

9 

355 

303 

295 

287 

279 

272 

264 

256 

248 

240 

232 

1 

0.9 

356 

224 

216 

209 

201 

193 

185 

177 

169 

161 

154 

2 

1.8 

357 

146 

138 

130 

122 

114 

106 

099 

091 

083 

o75 

3 

2-7 

358 

067 

060 

052 

044 

036 

028 

021 

013 

005 

*997 

4 

3-6 

359 
0.360 

361 

0.24989 

982 

974 

966 

958 

951 

943 

935 

927 

920 

5 
6 
7 
8 

9 

4-5 
5-4 
6.3 
7-2 
8.1 

912 

904 

896 

889 

881 

873 

865 

s5.^ 

850 

842 

835 

827 

819 

S11 

804 

796 

788 

78i 

773 

765 

362 

758 

750 

742 

734 

727 

719 

7" 

704 

696 

688 

363 

681 

673 

666 

658 

650 

643 

63! 

627 

620 

612 

3<J4 

604 

597 

589 

582 

574 

566 

559 

55i 

544 

536 

365 

528 

521 

513 

506 

498 

490 

483 

475 

468 

460 

8 

366 

453 

445 

438 

430 

422 

415 

407 

400 

392 

385 

3^7 

377 

370 

362 

355 

347 

340 

332 

325 

317 

310 

2 

1.6 

368 

302 

29! 

287 

280 

272 

265 

257 

250 

242 

235 

3 

4 
5 
6 
7 

2.4 
3-2 
4.0 

4.8 
5-6 

369 
0.370 

37i 

227 

220 

212 

205 

197 

190 

182 

175 

168 

160 

153 

145 

138 

130 

123 

116 

108 

IOI 

093 

086 

078 

071 

064 

056 

049 

041 

034 

027 

019 

012 

372 

004 

*997 

*99<> 

*982 

*975 

*9^S 

*9&o 

*953 

*94& 

*938 

8 

6.4 

373 

0.23  931 

923 

916 

909 

901 

894 

887 

879 

872 

865 

9 

7.2 

374 

857 

850 

843 

836 

828 

821 

814 

806 

799 

792 

375 

784 

777 

77o 

763 

755 

748 

741 

733 

726 

719 

376 

712 

704 

697 

690 

683 

675 

668 

661 

654 

646 

377 

639 

632 

625 

617 

610 

603 

596 

589 

58i 

574 

7 

378 

567 

560 

553 

545 

538 

531 

524 

517 

509 

502 

1 

0.7 

379 
0.380 

381 

495 

488 

481 

474 

466 

459 

452 

445 

438 

431 

2 

3 
4 

5 

1.4 
2.1 

2.8 
3-5 

423 

416 

409 

402 

395 

3S8 

381 

373 

366 

359 

352 

345 

338 

331 

324 

317 

3'  "J 

302 

295 

288 

382 

281 

274 

267 

260 

253 

246 

238 

231 

224 

217 

6 

4.2 

383 

210 

203 

196 

189 

182 

175 

168 

161 

154 

M7 

7 

4-9 

384 

140 

133 

126 

119 

112 

105 

098 

091 

083 

076 

8 

5.6 

385 

069 

062 

055 

048 

041 

034 

027 

020 

013 

006 

9 

6-3 

386 

000 

*993 

*986 

*979 

*972 

*9^5 

*958 

*95i 

*944 

*937 

387 

0.22  930 

923 

916 

909 

902 

895 

888 

881 

874 

867 

388 

860 

853 

847 

840 

833 

826 

819 

812 

805 

70S 

389 
0.390 

39i 

791 

784 

777 

771 

764 

757 

750 

743 

736 

729 

6 

722 

716 

709 

702 

69! 

688 

681 

674 

667 

661 

1 
2 
3 

0.6 
1.2 
1.8 

654 

647 

640 

633 

626 

620 

613 

606 

599 

592 

392 

585 

579 

572 

565 

558 

55i 

545 

538 

531 

524 

4 

2.4 

393 

517 

5" 

504 

497 

490 

483 

477 

470 

463 

456 

5 

3.0 

394 

45o 

443 

436 

429 

422 

416 

409 

402 

395 

389 

6 

3-6 

395 

382 

375 

369 

362 

355 

348 

342 

335 

328 

321 

7 
8 

4.2 
4.8 
5-4 

396 

315 

308 

301 

295 

288 

281 

2  74 

268 

261 

254 

397 

248 

241 

234 

228 

221 

214 

208 

201 

194 

188 

9 

398 

181 

174 

1 63 

161 

154 

148 

Mi 

134 

128 

121 

399 
0.400 

114 

108 

IOI 

094 

,,s> 

081 

07J 

I.I..S 

0(1 1 

055 

n.220  1- 

04] 

035 

028 

022 

015 

008 

002 

*<>95 

#989 

A 

B  0 

' 

2    3 

1 

5 

6    7    8  |  9 

P  P 

a>l 

Put  a 

j  =  log  a  —  log  6. 

If  a 

>.3 

then 

x  =  A 

and   log  (a  —  0)  - 

log  a  —  B. 

If  a 

<  .  3 

then 

.,:        11 

and    Log  (a— b)  = 

log  a  — A. 

81 


SUBTRACTION. 

A 

B  0 

1 

2 

3 

4 

5  1 

H 

9 

P  P 

0.400 

401 
402 
403 

0.22  048 

041 

035 

028 

022 

015 

00  S 

002 

*995 

*98g 

0.21  982 
916 

851 

975 
910 
844 

969 
903 

838 

962 
897 

831 

956 
890 

825 

949 

8S4 
818 

943 

877 
812 

936 
870 
805 

929 
864 

799 

923 

857 
792 

404 
405 
406 

786 
721 
656 

779 
714 
649 

772 
708 
643 

766 
701 
636 

759 
69! 
630 

753 
688 
623 

746 
682 
617 

740 
675 
611 

733 
669 
604 

727 
662 
598 

407 
408 
409 

0.410 

411 

412 
413 

59i 
527 
463 

58! 
521 
456 

578 
5i4 
45o 

572 
508 
444 

565 
501 
437 

559 
495 
431 

553 
4S8 
425 

546 
482 
418 

540 
476 
412 

533 
469 
405 

1 
2 
3 
4 
5 
6 
7 

7 

0.7 
1.4 

2.1 

2.8 

3-5 
4.2 

4-9 

399 

393 

386 

380 

374 

3£>7 

361 

355 

348 

342 

336 
272 
209 

329 
266 
203 

323 
260 
197 

317 
253 
190 

310 
247 
184 

304 
241 

178 

298 
234 
171 

291 
228 
165 

285 
222 
159 

279 
215 
153 

414 
4i5 
416 

146 
084 
021 

140 

o77 
015 

i34 
071 
009 

127 
065 
003 

121 
059 

*99& 

"5 

052 
*99" 

109 

046 

*9S4 

102 
040 

*978 

096 

034 
*972 

090 

028 

*965 

8 
9 

5-6 
6-3 

4i7 
418 
419 

0.420 

421 
422 
423 

0.20  959 
897 
836 

953 
891 
829 

947 

885 
823 

941 

879 
817 

934 
873 
811 

928 
866 
805 

922 
860 
799 

916 

854 
793 

910 

S48 
786 

903 

842 
780 

774 

768 

762 

756 

750 

743 

737 

731 

725 

719 

'   713 
652 
59i 

707 
646 

585 

701 
640 
579 

69I 
634 

573 

688 
628 
567 

682 
621 
56i 

676 
615 

555 

670 
609 
549 

664 
603 
543 

658 

597 
537 

1 

6 
0.6 

424 
425 
426 

53i 
470 
410 

525 
464 
404 

5i8 
458 
398 

512 
452 
392 

506 
446 
386 

500 
440 

380 

494 
434 

374 

488 
428 
368 

482 
422 
362 

476 
416 

356 

2 
3 
4 

1.2 

1.8 
2.4 

427 
428 
429 

0.430 

43i 
432 
433 

350 
29 1 
231 

344 

285 
225 

338 
279 
219 

332 
273 
213 

326 
267 
207 

320 
261 
201 

314 
255 
196 

308 
249 
190 

302 
243 
184 

297 
237 
178 

5 
6 
7 
8 
9 

3.o 

3-6 
4.2 
4.8 
5-4 

172 

166 

160 

154 

148 

142 

136 

131 

125 

119 

113 

054 
0.19  996 

107 
048 
990 

IOI 

042 
984 

095 
037 

978 

089 
031 
972 

083 
025 
966 

078 
019 
960 

072 
013 
955 

066 
007 
949 

060 
001 
943 

434 
435 
436 

937 
879 
821 

931 

873 
815 

926 

867 
809 

920 

862 
804 

914 

856 
798 

908 
850 
792 

902 

844 
786 

896 

838 

781 

891 
833 
775 

885 
827 
769 

1 

5 

0.5 

437 

438 

439 

0.440 

441 
442 

443 

763 
706 
648 

758 
700 
643 

752 
694 
637 

746 
689 
631 

740 
683 
626 

735 
677 
620 

729 
671 
614 

723 
666 
608 

7i7 
660 
603 

712 
654 
597 

2 
3 
4 
5 
6 
7 
8 

9 

1.0 

i-5 
2.0 
2-5 
3-o 
3-5 
4.0 
4-5 

59i 

586 

580 

574 

569 

5^3 

557 

552 

546 

540 

534 
47S 
421 

529 
472 
416 

523 
466 
410 

517 
461 
404 

512 
455 
399 

506 
450 
393 

500 
444 
387 

495 
438 
382 

489 
433 
376 

483 
427 
37i 

444 
445 
446 

365 
309 
253 

359 
303 

247 

354 
298 
242 

348 
292 
236 

343 
297 
231 

337 
281 

225 

331 
275 
220 

326 
270 
214 

320 
264 
208 

315 
259 
203 

447 

448 

449 

0.450 

197 
142 

087 

192 
136 
081 

186 
131 
076 

181 

125 
070 

175 
120 
064 

170 
114 
059 

164 
109 
053 

158 
103 
048 

153 
098 
042 

M7 
092 
037 

3.19  031 

026  020 

015 

009  1  004 

1=999 

*993  =1 

9S8  *982 

A 

B  0 

1    2 

3 

4  J  5 

6    7    8    9 

P   P 

a>b.        Put  a;— loga  —  log b. 
Ifa;>.3,    then   x=  A        aud    log  (a — b)  =  log  a  —  B. 
If«<.3,    then   x  =  B        and   log  (a  —  6)  =  log  a  —  A. 

SUBTRACTION. 

A 

B  0 

1  |  2    3  | 

~> 

<; 

7  |  8  j  9 

P  P 

0.450 
4?i 

0.19  031 

026 

020 

015 

009 

004 

*999 

*993 

*gss 

*9S2 

0.18  977 

97i 

966 

960 

955 

949 

944 

938 

933 

927 

452 

922 

916 

911 

9°5 

900 

89! 

889 

884 

878 

873 

453 

867 

862 

S56 

S51 

S46 

840 

835 

S29 

824 

818 

454 

813 

808 

802 

797 

791 

786 

781 

775 

77" 

7<>4 

455 

759 

754 

748 

743 

737 

732 

727 

721 

716 

710 

456 

705 

700 

694 

689 

683 

67S 

673 

667 

662 

657 

6 

457 

651 

646 

641 

635 

630 

624 

619 

614 

608 

603 

1 

0.6 

458 

598 

592 

587 

582 

576 

571 

566 

560 

555 

550 

2 

1.2 

459 
0.460 

461 

544 

539 

534 

528 

523 

518 

512 

507 

502 

496 

3 
4 
5 
6 

1.8 
2.4 
3-0 

3-6 

491 

486 

481 

475 

470 

465 

459 

454 

449 

443 

438 

433 

42S 

422 

417 

412 

406 

401 

396 

391 

462 

385 

380 

375 

37o 

3<J4 

359 

354 

349 

343 

338 

7 

4.2 

4<J3 

333 

328 

322 

317 

312 

307 

301 

296 

291 

286 

8 

4.8 

4' '4 

280 

275 

270 

265 

259 

254 

249 

244 

239 

233 

9 

5-4 

4"5 

228 

223 

218 

212 

207 

202 

J97 

192 

186 

181 

466 

176 

171 

166 

160 

155 

150 

145 

140 

135 

129 

467 

124 

119 

114 

109 

103 

098 

093 

088 

083 

078 

468 

072 

067 

062 

057 

052 

047 

042 

036 

031 

026 

469 
0.470 

47i 

021 

016 

on 

006 

000 

*995 

*99° 

*985 

*98o 

*975 

5 

0.1797" 

964 

959 

954 

949 

944 

939 

934 

929 

924 

918 

9*3 

908 

903 

898 

>s<)3 

888 

883 

878 

873 

472 

867 

862 

857 

852 

S47 

842 

837 

832 

827 

822 

1 

"•5 

473 

817 

812 

807 

801 

796 

791 

786 

781 

776 

771 

2 
3 

4 
5 
6 

1.0 

i-5 
2.0 

474 

766 

761 

756 

75i 

746 

741 

736 

73i 

726 

721 

475 

716 

7ii 

706 

700 

695 

690 

685 

680 

675 

670 

2.5 

476 

665 

660 

655 

650 

645 

640 

635 

630 

625 

620 

3-o 

477 

615 

610 

605 

600 

595 

590 

585 

580 

575 

57o 

7 

3-5 

478 

565 

560 

555 

55o 

545 

54o 

535 

530 

525 

520 

8 

4.0 

479 
0.480 

481 

515 

5" 

506 

5oi 

496 

491 

486 

4S1 

476 

471 

9 

4-5 

466 

461 

456 

45i 

446 

441 

436 

431 

426 

421 

416 

412 

4"7 

402 

397 

392 

387 

382 

377 

372 

482 

367 

362 

357 

352 

348 

343 

338 

333 

328 

323 

483 

318 

313 

308 

303 

299 

294 

289 

284 

279 

274 

484 

269 

264 

259 

255 

250 

245 

240 

235 

230 

225 

485 

220 

216 

211 

206 

201 

196 

191 

186 

182 

177 

486 

172 

167 

162 

157 

153 

148 

143 

138 

133 

128 

4 

487 

123 

119 

114 

109 

104 

099 

09! 

090 

085 

0S0 

1 

0.4 

488 

075 

070 

06C 

061 

056 

051 

046 

042 

037 

032 

2 

0.8 

489 
0.490 

49' 

027 

022 

018 

013 

008 

003 

*998 

*994 

*989 

*984 
936 

3 
4 
5 
6 

1.2 
1.6 

2.0 

2.4 

0.16979 

974 

970 

9<>5 

960 

955 

<>5i 

946 

■14" 

931 

927 

922 

917 

912 

908 

903 

898 

893 

-■-.. 

492 

884 

879 

874 

870 

865 

860 

855 

851 

846 

841 

7 

2.8 

493 

836 

832 

827 

822 

818 

813 

808 

803 

799 

794 

8 

3-2 

494 

789 

784 

7  So 

775 

770 

766 

761 

756 

75i 

747 

9 

3-6 

495 

742 

737 

733 

728 

723 

719 

714 

709 

704 

7"" 

496 

695 

690 

686 

681 

676 

672 

667 

662 

658 

653 

497 

648 

644 

639 

''34 

630 

625 

620 

616 

611 

606 

498 

602 

597 

592 

588 

533 

?7> 

5  74 

569 

564 

560 

499 
0.500 

555 

55i 

541 

537 

532 

52  7 

523 

518 

5£3 

>.!<>  509 

504 

500 

495 

490 

1-' 

4Si 

177 

472 

i"7 

A 

B  0  i  1 

2    3    I 

5 

6  |  7  |  8  |  9 

J'  P 

a  >  b.        Put  x  =  \oga  —  log 6. 

if'-  .:<,   then  x-A       and   log  (a— 6)=  log  a   /»'. 

I  !'.»■■  .3,  -then   x  -   li       and   log  (a— b)  =  log  a— A. 

33 


SUBTRACTION. 

A 

B  0 

1 

0 

3 

4 

5 

6 

7 

8 

'.i 

P  P 

0.50 
5i 

0.16  509 

463 

417 

371 

325 

2  So 

234 

1S9 

144 

>••,•> 

054 

009 

*9^5 

*92i 

*876 

*832 

*783 

*745 

*7Qi 

*057 

46 

45 

44 

43 

52 

0.15  614 

57i 

52S 

485 

442 

400 

357 

3i| 

273 

230 

1 

4.6 

4-5 

4.4 

4-3 

53 

189 

147 

105 

064 

1)22 

*9Si 

*94Q 

*899 

*858 

*8i7 

2 

9.2 

9.0 

8.8 

8.6 

54 

0.14777 

736 

696 

656 

616 

576 

536 

496 

457 

417 

3 

13-8 

13-5 

13-2 

12.9 

55 

373 

339 

300 

261 

222 

183 

145 

106 

068 

030 

4 

18.4 

1S.0 

17.6 

17.2 

56 

0.13  992 

954 

916 

878 

84O 

803 

766 

728 

691 

654 

5 

23-0 

22.5 

22.0 

21-5 

57 

617 

58i 

544 

507 

471 

435 

393 

362 

326 

291 

6 

27.6 

27.0 
31-5 
36.0 

4<J-5 

26.4 
30.8 
35-2 
39-6 

25.8 

53 

25I 

219 

184 

148 

"3 

078 

043 

008 

*973 

*938 

7 
8 
9 

32.2 
36.8 
41.4 

30.1 
34-4 

38.7 

59 

0.12  903 

869 

834 

800 

766 

732 

698 

664 

630 

596 

0.60 

61 

563 

529 

496 

463 

429 

396 

363 

330 

298 

265 

232 

200 

168 

135 

103 

071 

039 

007 

*975 

*944 

42 

41 

40 

39 

62 

0.11  912 

880 

849 

818 

786 

755 

724 

693 

663 

632 

1 

4.2 
8.4 

4.1 
8.2 

4.0 

8.0 

3-9 

7.8 

63 

601 

571 

540 

5io 

479 

449 

419 

389 

359 

329 

2 

64 

299 

270 

240 

211 

181 

152 

123 

094 

065 

036 

3 

4 
5 
6 

12.6 

16.8 

12.3 
16.4 

12.0 
16.0 

11. 7 
15.6 

65 

007 

*978 

*949 

*92i 

*8g2 

^864 

*835 

*8o7 

*779 

*75<> 

21.0 

20.5 
24.6 

20.0 

i')-5 
23-4 

66 

0.10  722 

694 

667 

639 

611 

'583 

556 

528 

501 

474 

25.2 

24.0 

67 

440 

419 

392 

365 

338 

312 

285 

258 

231 

205 

7 

29.4 

28.7 

28.0 

27-3 

68 

178 

152 

126 

IOO 

073 

047 

021 

*995 

*97Q 

*944 

8 

33-6 

32.8 

32.0 

31.2 

69 
0.70 

0.09  918 

893 

867 

842 

816 

791 

766 

740 

715 

690 

9 

37-8 

36.9 

36.0 

35-1 

665 

640 

616 

591 

566 

542 

517 

493 

468 

444 

38 

37 

36 

35 

71 

420 

395 

371 

347 

323 

299 

275 

252 

228 

204 

1  "  c 

3-6 

72 

181 

157 

134 

no 

087 

064 

041 

018 

*995 

*972 

3-° 

7.6 
1 1.4 

15-2 

3-7 

3-5 

73 

0.08  949 

926 

903 

880 

858 

835 

813 

790 

768 

745 

2 
3 

4 

7-4 

7-2 

10.8 

7.0 
10.5 
14.0 

74 

723 

701 

679 

657 

635 

613 

591 

569 

547 

525 

i4'8 

14.4 

75 

504 

482 

461 

439 

418 

396 

375 

354 

333 

3" 

5 

19.0 

18.5 

18.0 

17-5 

76 

290 

269 

248 

228 

207 

186 

165 

M5 

124 

103 

6 

22.S 

21.6 

21.0 

77 

083 

063 

042 

022 

002 

^98 1 

•*g6i 

*94i 

*92i 

*9°i 

7 

26.6 

25-9 

25.2 

24-5 

78 

0.07  881 

861 

842 

822 

802 

782 

763 

743 

724 

704 

8 

30.4 

29.6 

28.8 

28.0 

79 
0.80 

685 

666 

646 

627 

608 

589 

570 

551 

532 

513 

9 

34-2 

33-3 

32.4 
32 

3-2 

31.5 

31 

3-i 

494 

475 

456 

438 

419 

401 

382 

363 

345 

327 

Oi           Qt 

81 

308 

290 

272 

253 

235 

217 

199 

181 

163 

145 

I 

3-4 

3-3 

82 

127 

no 

092 

074 

056 

039 

021 

004 

*986 

*9&9 

_' 

6.8 

6.6 

6.4 

6.2 

83 

0.06951 

934 

917 

900 

882 

865 

S48 

831 

814 

797 

3 

10.2 

9-9 

9.6 

9-3 

84 

780 

763 

747 

73o 

713 

696 

680 

663 

647 

630 

1 

13.6 

13.2 

12.8 

12.4 

85 

614 

597 

58i 

564 

548 

532 

5i6 

499 

4S3 

467 

3 

17.0 

16.5 

16.0 

15-5 

86 

451 

435 

419 

403 

337 

372 

356 

340 

324 

309 

6 

20.4 

19.8 

19.2 

1S.6 

87 

293 

27S 

262 

247 

231 

216 

200 

185 

170 

155 

7 

23.8 

23.1 

22.4 

21.7 

88 

139 

124 

109 

094 

079 

064 

049 

034 

019 

004 

8 

27.2 

26.4 

25.6 

24. S 

89 
0.90 

91 

0.05  989 

975 

960 

945 

931 

916 

901 

887 

872 

858 

9 

30.6 

29.7 

28.8 

28 

28 

27.9 

27 
2.7 

844 

829 

815 

800 

786 

772 

758 

744 

730 

715 

QA    9Q 

701 

6S7 

673 

659 

646 

632 

618 

604 

590 

577 

I 

3-o 

2.9 

92 

563 

549 

536 

522 

509 

495 

482 

468 

455 

441 

2 

6.0 

5-8 

5-6 

5-4 

93 

428 

415 

401 

388 

375 

362 

349 

336 

323 

310 

3 

9.0 

8.7 

8.4 

8.1 

94 

297 

284 

271 

258 

245 

232 

219 

207  j  194 

181 

4 

12.0 

11.6 

n. 2 

10.8 

95 

169 

156 

143 

131 

118 

106 

093 

081   069 

056 

5 

15-0 

14.5 

14.0 

13-5 

96 

044 

032 

019 

007 

*995 

*983 

*97Q 

*958 

*94& 

*934 

6 

18.0 

17-4 

16.8 

16.2 

97 

0.04  922 

910 

898 

886 

874 

863 

851 

839 

827 

815 

7 

21.0 

20.3 

19.6 

18.9 
21.6 

98 

804 

792 

780 

769 

757 

746 

734 

723 

711 

700 

8 

24.0 

23.2 
26.1 

22.4 

99 
1.00 

688 

677 

666 

654 

643 

632 

620 

609 

598 

587 

9 

27.0 

2?.2 

24-3 

0.04  576 

565 

554 

543 

532 

52i 

510 

499 

488 

477 

A 

B  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P  P 

a  >  b. 

Put 

x  =  l 

og  a  — log  b. 

If  a 

7  >  .  3,   then 

x  —  A 

anc 

1   log  (a  —  b)=\og  a — B. 

If  a 

5  <  .  3,   then 

x  =  B 

and 

log  (a  —  6)= log  a  —  A. 

SUBTRACTION. 

A 

B  0 

1 

2 

3 

4 

5 

6 

7  |  8 

9 

P  P 

1.00 

>.04  576 

5t>5 

554 

543 

532 

521 

510 

499 

4SS 

477 

20 
2.6 

9^ 

24 

2.4 

23 

2.3 

OI 

466 

455 

444 

434 

423 

412 

402 

391 

380 

370  j 

2-5 

02 

359 

349 

338 

328 

317 

3°7 

296 

286 

275 

265   . 

5-2 

5-o 

4.8 

4.6 

03 

255 

245 

234 

224 

214 

204 

194 

183 

173 

163  \ 

7.8 

7-5 

7.2 

6.9 

04 

153 

143 

133 

123 

113 

103 

093 

084 

074 

064   ~ 

10.4 

10.0 

9.6 

9.2 

05 

054 

044 

o35 

025 

015 

006 

*99^ 

*9S6 

*977 

*967  5 

13-0 

12.5 

12.0 

ii-5 

06 

0.03  958 

948 

938 

929 

920 

910 

901 

891 

882 

873  ( 

15-6 

15.0 

14.4 

13.8 

07 

863 

854 

845 

835 

S26 

817 

808 

799 

790 

781  7 

18.2 

17.5 

16.8 

16.1 

08 

77i 

762 

753 

744 

735 

726 

717 

708 

700 

691  s 

20.8 

20.0 

19.2 

18.4 

09 
1.10 

II 

682 

673 

664 

655 

647 

638 

629 

620 

612 

603  Q 

5i8 

23-4 

22.5 

21.6 

20.7 

594 

586 

577 

569 

560 

552 

543 

535 

526 

509 

501 

492 

484 

476 

467 

459 

45i 

443 

434 

22 

21 

20 

19 

12 

426 

418 

410 

402 

393 

385 

377 

369 

361 

353  1 

1  2.2 

2.1 

2.0 

1.9 

l3 

345 

337 

329 

321 

313 

305 

297 

289 

282 

274  2 

4-4 

4.2 

4.0 

3-8 

M 

266 

258 

250 

243 

235 

227 

219 

212 

204 

196  3 

1  6.6 

8.8 

6.3 

8.4 

6.0 
8.0 

5-7 
7.6 

15 

189 

181 

174 

166 

159 

151 

143 

136 

128 

121  4 

16 

114 

106 

099 

091 

084 

077 

069 

062 

055 

047  i 

1 1.0 

13.2 

10.5 
12X 

12.0 

9-5 
1 1.4 

17 

040 

o33 

026 

018 

on 

004 

*997 

*99° 

*983 

*97&  . 

15-4 

14-7 

14.0 

13-3 

18 

0.02  969 

961 

954 

947 

940 

933 

926 

919 

912 

906  I 

17.6 

16.S 

16.0 

15-2 

19 

1.20 

21 

899 

892 

885 

878 

871 

864 

S58 

851 

844 

337  c 

19.8 

18.9 

18.0 

17.1 

830 

824 

817 

810 

804 

797 

790 

784 

777 

771 

764 

757 

75i 

744 

738 

73i 

725 

718 

712 

705 

18 

17 

16 

15 

22 

699 

693 

686 

680 

674 

667 

661 

655 

648 

642  ] 

1.8 

1.7 

1.6 

1  .'5 

23 

636 

629 

623 

617 

611 

605 

598 

592 

536 

58o   J 

3-6 

3-4 

3-2 

3.o 

24 

574 

568 

562 

556 

55o 

544 

538 

532 

526 

520  : 

5-4 

5-i 

4.8 

4-5 

25 

5U 

508 

502 

496 

490 

4S4 

478 

472 

466 

461  - 

1.  7-2 

6.8 

6.4 

6.0 

26 

455 

449 

443 

437 

432 

426 

420 

414 

409 

403  - 

9.0 

8-5 

8.0 

7-5 

27 

397 

392 

386 

380 

375 

369 

363 

358 

352 

347  ( 

>  10.8 
j   12.6 
5  14.4 
)  16.2 

10.2 

II.C 

i3-£ 

IS." 

9.6 
11. 2 

9.0 
10.5 

28 

34i 

336 

330 

325 

319 

314 

308 

303 

297 

292 

12.8 

12.0 

29 
1.30 

31 

286 

281 

276 

270 

265 

260 

254 

249 

244 

238  | 

14.4 

13-5 

233 

228 

223 

217 

212 

207 

202 

196 

191 

186 

181 

176 

171 

166 

160 

155 

150 

145 

140 

135 

14 

13 

12 

11 

32 

130 

125 

120 

"5 

no 

105 

100 

095 

090 

085 

[  1.4 

1.' 

1.2 

1.1 

33 

080 

o75 

071 

066 

061 

056 

051 

046 

042 

037 

2  2.8 

2.1 

>  2.4 

2.2 

34 

032 

027 

022 

018 

013 

008 

003 

*999 

*994 

*989 

3  4-2 

3-< 

3-f 

3-3 

35 

0.01  985 

980 

975 

97i 

966 

961 

957 

952 

948 

943 

1  5-t 

5- 

4.8 

4-4 

36 

938 

934 

929 

92! 

920 

916 

911 

907 

902 

898 

5  7.C 

6.f 

6.c 

5-5 

37 

893 

889 

884 

880 

876 

871 

867 

862 

858 

854 

b     i.t 

7-1 

7-2 

8-4 

1   9.e 
10.8 

6.6 

I    38 

849 

845 

841 

836 

832 

828 

823 

819 

81! 

811 

1     9-8 

9.] 

7-7 
8.8 
0.0 

39 
1.40 

41 

806 

802 

798 

794 

789 

785 

781 

777 

773 

768 

5  11. 2 
T  12.6 

io.<: 
ti  .■ 

764 

760 

756 

752 

748 

711 

740 

736 

73i 

727 

J   *•*•**  —  •   —   ^ -j 

723 

719 

715 

7" 

707 

703 

699 

695 

691 

687 

9 

8 

7 

3  5 

42 

6S3 

679 

675 

672 

668 

(,64 

660 

656 

652 

648 

i  0.9 
2  1.8 

n.S 

3.7  0 

6  0.5 

43 

644 

640 

637 

f>33 

629 

O25 

621 

618 

614 

610 

1.6 

1.4  1 

2  1.0 

44 

606 

602 

599 

595 

591 

587 

584 

580 

576 

573 

3  2.7 

2-4 

2.1  1 

8  1.5 

45 

569 

565 

562 

558 

554 

551 

547 

543 

540 

536 

+  3-6 

3-2 

2.8  2 

4  2.0 

46 

533 

529 

525 

522 

518 

515 

5" 

508 

504 

501 

5  4-5 

4.0 

3-5  3 

0  2.5 

47 

497 

494 

490 

487 

483 

4S0 

476 

473 

469 

466 

6  5-4 

4.8 

4-2  3 

6  3.0 

48 

462 

459 

456 

452 

449 

445 

442 

439 

435 

432 

7  6.3 

5-6 

+•9  4 

2  3-5 

49 

429 

425 

422 

419 

415 

412 

409 

405 

402 

;,.»> 

3  7.2 
9  8.1 

6.4 

5.6  4 
5-3  5 

8  4.0 
4  4-5 

1.50 

ci. mi  396 

392 

389 

386 

383 

379 

376 

373 

37o 

366 

7'2 

A 

1',  0 

1 

2 

3 

4 

5 

6  |  7  |  8  |  9 

r  P 

a  >  b.        Put  re— log  a  —  log  b. 

If'.r   ..",,    then   x=A        and   log  (a 

—b)=  \oga  —  B. 

If  ;*;■'.:>,    then   x  =  B        and   log  (a 

—  b)  =  log  a  —  A . 

36 


SUBTRACTION. 

A 

B  0 

_u 

6  I  • 

7 

H 

<t 

P  P 

150 

5i 

j.oi  396 

392 

389 

386  1  383 

379 

376 
344 

373 

37o 

366 

363 

360 

357 

354 

35i 

347 

341 

338 

335 

52 

332 

329 

326 

322 

319 

316 

313 

310 

307 

304 

53 

301 

298 

295 

292 

289 

286 

283 

280 

277 

274 

54 

271 

268 

265 

262 

259 

256 

253 

250 

247 

244 

4 

55 

242 

239 

236 

233 

230 

227 

224 

221 

219 

216 

1 

0.4 

56 

213 

210 

207 

204 

202 

199 

196 

193 

190 

188 

2 

0.8 

57 

185 

182 

179 

177 

174 

171 

168 

166 

j  63 

160 

3 

1.2 

58 

158 

i55 

152 

150 

M7 

144 

142 

139 

136 

134 

4 

1.6 

59 

1.60 

61 

131 

128 

126 

123 

120 

118 

115 

113 

no 

107 

5 
6 
7 
8 
9 

2.0 
2.4 
2.8 
3-2 
%.6 

0.01  105 

102 

100 

097 

09! 

092 

089 

087 

084 

082 

079 

077 

074 

072 

069 

067 

064 

062 

059 

o57 

62 

054 

052 

050 

047 

045 

042 

040 

037 

035 

033 

63 

030 

028 

025 

023 

021 

018 

016 

014 

on 

009 

64 

006 

004 

002 

*999 

*997 

*995" 

*993 

*99° 

*988 

*986 

65 

0.00983 

981 

979 

976 

974 

972 

970 

967 

965 

963 

66 

961 

958 

956 

954 

952 

950 

947 

945 

943 

94r 

67 

939 

93f> 

934 

932 

930 

928 

926 

923 

921 

919 

68 

917 

91! 

913 

911 

908 

906 

904 

902 

900 

898 

69 
1.70 

7i 

896 

894 

892 

890 

888 

886 

883 

881 

879 

877 

3 

0.00  875 

873 

871 

869 

867 

865 

863 

861 

859 

857 

855 

853 

851 

849 

847 

845 

843 

841 

839 

837 

1 

0.3 

•72 

836 

834 

832 

830 

828 

826 

824 

822 

820 

818 

2 

0.6 

73 

816 

814 

813 

811 

809 

807 

805 

803 

801 

799 

3 

0.9 

74 

798 

796 

794 

792. 

790 

788 

787 

785 

783 

781 

4 

5 
6 

1.2 

1-5 
1.8 

75 

779 

777 

776 

774 

772 

770 

768 

767 

765 

763 

76 

761 

760 

758 

756 

754 

753 

751 

749 

747 

746 

7 

2.1 

77 

744 

742 

740 

739 

737 

735 

734 

732 

730 

728 

8 

2.4 

78 

727 

725 

723 

722 

720 

7i8 

7i7 

715 

713 

712 

9 

2.7 

79 

1.80 

81 

710 

708 

707 

705 

704 

702 

700 

699 

697 

695 

0.00  694 

692 

691 

689 

687 

6S6 

684 

683 

681 

679 

678 

676 

675 

673 

672 

670 

669 

667 

665 

664 

82 

662 

661 

659 

658 

656 

655 

653 

652 

650 

649 

83 

647 

646 

644 

643 

641 

640 

638 

637 

635 

634 

84 

632 

631 

629 

628 

626 

625 

624 

622 

621 

619 

85 

618 

616 

615 

614 

612 

611 

609 

608 

606 

605 

86 

604 

602 

601 

599 

598 

597 

595 

594 

593 

591 

87 

590 

588. 

587 

586 

584 

583 

582 

580 

579 

578 

88 

576 

575 

574 

572 

57i 

570 

568 

567 

566 

564 

Z 

89 
1.90 

91 

563 

562 

56i 

559 

558 

557 

555 

554 

553 

55i 

1 
2 
3 
4 
5 
6 

0.2 
0.4 
0.6 
O.8 

0.00  550 

549 

548 

546 

545 

544 

543 

54i 

54o 

539 

538 

536 

535 

534 

533 

53i 

530 

529 

528 

527 

92 

525 

524 

523 

522 

520 

519 

5iS 

517 

5i6 

514 

" 

93 

513 

512 

511 

5io 

509 

507 

506 

505 

504 

503 

7 

1.4 

94 

502 

500 

499 

498 

497 

496 

495 

493 

492 

491 

8 

1.6 

95 

490 

489 

488 

487 

486 

484 

483 

482 

481 

480 

9 

1.8 

96 

479 

478 

477 

476 

474 

473 

472 

47i 

470 

469 

97 

468 

467 

466 

465 

464 

462 

461 

460 

459 

458 

98 

457 

456 

455 

454 

453 

452 

451 

45o 

449 

448 

99 
2.00 

447 

44b 

445 

444 

433 

443 

442 

441 

440 

439 

437 

0.00  436 

435 

434 

432 

43i 

430 

429 

428 

427 

A 

B  0  |  1  j  2  |  3 

4 

5 

6  j  7    8 

9 

P  P 

a  >  b.        Put  x  =  log  a  —  log  b. 

If  x  >  .  3,   then   x  =  A        and   log  Ta  —  b)=  log  a  —  B. 

If  x  <  .  3,   then   x  =  B        and   log  (a  —  b)  =  log  a  —  A . 

3fi 


SUBTRACTION. 

A 

B    0 

1 

I     2 

3 

4 

5 

6 

7 

8 

9 

p  p 

2.0 

i 

o.oo  436 

426 

417 

407 

398 

389 

380 

371 

363 

354 

9 

'    8 
0.8 

346 

338 

331 

323 

316 

309 

302 

29! 

288 

281 

1 

0.9 

2 

275 

269 

262 

256 

251 

245 

239 

234 

229 

223 

2 

1.8 

1.6 

3 

218 

213 

208 

204 

199 

194 

190 

186 

181 

177 

3 

2.7 
3-6 
4-5 
5-4 
6-3 
7.2 

2.4 

4 

173 

169 

165 

162 

158 

154 

151 

i47 

144 

141 

4 

5 
6 

3-2 

4.0 

4.8 
5.6 

6.4 

5 

138 

134 

131 

128 

125 

123 

120 

"7 

114 

112 

6 

109 

107 

104 

102 

100 

097 

095 

093 

091 

089 

7 

8 

7 

087 

085 

083 

081 

079 

077 

076 

074 

072 

070 

8 

069 

067 

066 

064 

063 

061 

060 

059 

057 

056 

9 

8.1 

7.2 

9 
3.0 

055 

053 

052 

051 

050 

049 

048 

047 

046 

044 

0.00  043 

042 

041 

041 

040 

039 

038 

o37 

036 

035 

7 

6 

0.6 

5 

0.5 

035 

034 

033 

032 

031 

031 

030 

029 

029 

028 

I 

0.7 

2 

027 

027 

026 

026 

025 

024 

024 

023 

023 

022 

2 

1.4 

1.2 

1.0 

3 

022 

021 

021 

020 

020 

019 

019 

019 

018 

018 

3 

2.1 

1.8 

i-5 

4 

017 

017 

017 

016 

016 

015 

015 

015 

014 

014 

4 

2.8 

2.4 

2.0 

5 

014 

013 

013 

013 

013 

012 

012 

012 

on 

on 

5 

3-5 

3-o 

2-5 

6 

on 

on 

OIO 

OIO 

OIO 

OIO 

OIO 

009 

009 

009 

6 

4.2 

3-6 

3-o 

7 

009 

008 

008 

008 

008 

008 

008 

007 

007 

007 

7 
8 

4.9 

5-6 
6-3 

4.2 

4.8 

3-5 

8 

007 

007 

007 

006 

006 

006 

006 

006 

006 

006 

4.0 

9 

4.0 

i 

005 

005 

005 

005 

005 

005 

005 

005 

005 

004 

9 

5-4 

4-5 

0.00  004 

004 

004 

004 

004 

004 

004 

004 

004 

004 

003 

003 

003 

003 

003 

003 

003 

003 

003 

003 

1 

4 

0.4 
0.8 

0 

0.3 
0.6 

2 

003 

003 

003 

003 

002 

002 

002 

002 

002 

002 

2 

3 

002 

002 

002 

002 

002 

002 

002 

002 

002 

002 

3 

1.2 

0.9 

4 

002 

002 

002 

002 

002 

002 

002 

OOI 

OOI 

OOI 

4 

1.6 

1.2 

5 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

5 

2.0 

i-5 

6 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

6 

2.4 

1.8 

7 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

7 

2.8 

2.1 

8 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

OOI 

8 

3-2 

2.4 

9 
5.0 

OOI 

OOI 

OOI 

OOI 

OOO 

OOO 

OOO 

OOO 

OOO 

OOO 

9 

3-6 

2.7 

0.00  OOO 

OOO 

OOO 

OOO 

OOO 

OOO 

OOO 

OOO 

OOO 

OOO 

A 

B     0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P     P 

a>b, 

A  =  log  a  —  log  6,              log  (a  — 

b)= 

log  a  —  B. 

or 

B  =  log  a  —  log  b,             log  (a  — 

b)= 

log  a  —  A. 

The  above  tabl 

e  of  Subtraction  Logarithms  is  bast 

id  on 

the  identity 

/     °     ^ 

f      X 

^ 

log( 

%—b)  =  log 

X 

=  log  a  —  log 

) 

U- 

-1> 

where  x  =  -r- . 

0 

The  argument 

is  log  x ,  and  the  function  is  log  1  - 

X 

)• 

C  — 1 

A  is  the  argurr 

lent  and  B  the  function  when  log  x 

>.3 

,  and 

B  is  the  argum 

ent  and  A  the  function  when  log  x 

<.3 

37 


III 

TABLE  OF  THE    LOGARITHMS 

OF  THE 

TRIGONOMETRIC   FUNCTIONS 

FROM  0°  TO  1°  AND  89°  TO  90°  FOR  EVERY  SECOND, 

AND 

FROM  1°  TO  6°  AND  84°  TO  89°  FOR  EVERY  TEN  SECONDS. 

L  Cos      *90                L  Sin                        0°                      L  Tan             180°    *270° 

o.oo 

,  i 

0'< 

2" 

3" 

4" 

5" 

6"     |    7"     |    8" 

9" 

10" 

ooo 

)   0 

4.    _ 

6S557 

98660 

#16270 

4=28763 

*38454 

4=46373 

^53067 

*58866 

4=63982 

4=68557 

50 

ooo 

10 

s!  68557 

72697 

76476 

79952 

83170 

86167 

8S969 

91602 

94085 

96433 

98660 

40 

ooo 

20 

98660 

^0779 

#02800 

*°473Q 

*o6579 

*oS35i 

4=10055 

#11694 

*i3273 

4=14797 

#16270 

30 

ooo 

3" 

6. 16270 

17694 

19072 

20409 

21705 

22964 

24188 

25378 

26536 

27664 

28763 

20 

ooo 

4" 

28763 

29836 

30882 

3i904 

32903 

33879 

34833 

35767 

36682 

37577 

38454 

10 

ooo 

5° 

38454 

39315 

40158 

40985 

41797 

42594 

43376 

44145 

44900 

45643 

46373 

o59 

50 

ooo 

1  «. 

6.4  6373 

7090 

7797 

8492 

9175 

9849 

*°5I2 

4=1165 

#1808 

4=2442 

4=3067 

ooo 

1(1 

6.5  3067 

3683 

4291 

4890 

548i 

6064 

6639 

7207 

7767 

8320 

8866 

40 

ooo 

20 

8866 

9406 

9939 

*0465 

*ogS5 

4=1499 

*2007 

4=2509 

*3oo6 

4=3496 

4=3982 

30 

ooo 

30 

6.6  3982 

4462 

4930 

5406 

5870 

6330 

6785 

7235 

7680 

8121 

8557 

20 

ooo 

4" 

8557 

8990 

9418 

9841 

#0261 

#0676 

#IOSS 

*I496 

4=1900 

4=2300 

4=2697 

10 

ooo 

50 

6.7  2697 

3090 

3479 

3865 

4248 

4627 

5003 

5376 

5746 

6112 

6476 

o58 

ooo 

2  o 

6476 

6836 

7193 

7548 

7900 

8248 

8595 

8938 

9278 

9616 

9952 

50 

ooo 

w 

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353 

376 

398 

421 

37 

2 

4.6 

23 

421 

443 

466 

488 

5" 

533 

556 

36 

3 

6.9 

24 

556 

578 

601 

623 

646 

668 

691 

35 

4 

5 
6 

9.2 
11. 5 
13-8 
16.1 

25 

5gi 

713 

735 

758 

780 

802 

825 

34 

26 

825 

847 

869 

892 

914 

936 

959 

33 

7 

27 

959 

981 

*oo3 

*C25 

*Q48 

*°70 

*og2 

32 

8 

18.4 

28 

8.98  092 

114 

136 

159 

181 

203 

225 

3i 

9 

20.7 

29 

225 

247 

269 

291 

314 

336 

358 

30 

30 

358 

380 

402 

424 

446 

468 

490 

29 

1 

2.2 

3i 

490 

512 

534 

556 

578 

600 

622 

28 

2 

4.4 

6.6 

32 

622 

644 

666 

687 

709 

73i 

753 

27 

3 
4 

5 
6 

33 

753 

775 

797 

819 

841 

862 

884 

26 

8.8 

34 

884 

906 

928 

950 

971 

993 

*oi5 

25 

n.o 

13.2 

35 

8.99015 

037 

058 

080 

102 

123 

145 

24 

3& 

145 

167 

188 

210 

232 

253 

275 

23 

7 

15-4 

37 

275 

297 

3i8 

340 

361 

383 

405 

22 

8 

17.6 

38 

405 

426 

44S 

469 

491 

512 

534 

21 

9 

19.8 

39 

534 

555 

577 

598 

620 

641 

662 

20 

40 

662 

684 

705 

727 

748 

769 

79i 

19 

1 

6i 

2.1 

41 

79i 

812 

834 

855 

876 

898 

919 

18 

2 

4.2 
6-3 
8.4 

42 

919 

940 

961 

983 

*oo4 

*°25 

*<m6 

17 

43 

9.00  046 

06S 

089 

no 

131 

153 

174 

16 

4 

44 

174 

195 

216 

237 

258 

280 

301 

15 

5 
6 

10.5 
12.6 

45 

301 

322 

343 

364 

385 

406 

427 

M 

46 

427 

448 

469 

490 

5" 

532 

553 

13 

7 

14.7 

47 

553 

574 

595 

616 

637 

658 

679 

12 

8 

16.8 

48 

679 

700 

721 

742 

763 

784 

805 

11 

9 

18.9 

49 

805 

826  346 

867 

888 

909 

930 

10 

9f> 

50 

930 

951 

971 

992 

*oi3 

*Q34 

*°55 

9 

I 

2.0 

5i 

9-oi  055 

075 

096 

"7 

138 

158 

179 

8 

2 

4.0 

52 

179 

200 

220 

241 

262 

282 

303 

7 

3 

6.0 

53 

303 

324 

344 

365 

386 

406 

427 

6 

4 

8.0 

54 

427 

447 

468 

489 

509 

530 

550 

5 

5 
6 

1 0.0 
12.0 

55 

550 

571 

591 

612 

632 

653 

673 

4 

56 

673 

694 

714 

735 

755 

776 

796 

3 

7 

14.0 
16.0 
18.0 

57 

796 

816 

837 

857 

878 

898 

918 

2 

8 

5S 

918 

939 

959 

979 

#ooo 

*020 

*<MO 

1 

9 

59 

9.02  040  1  061 

081 

101 

121 

142 

162 

0 

60"   |  50" 

40" 

30" 

20" 

10" 

0" 

P  P 

-174°     2<U°     -'354c 


84° 


L  Cot 


L  Cos 

L 

Sin 

6° 

*96°  186°  *2 

?6° 

9-99 

i) 

10" 

20 

30" 

40" 

50" 

60" 

P  P 

761 

0 

9-01  923 

943 

964 

984 

*oo4 

*024 

*°43 

59 

760 

760 

1 

9.02  043 

063 

083 

103 

123 

143 

163 

58 

759 

759 

2 

163 

183 

203 

223 

243 

263 

283 

57 

757 

21 

757 

3 

283 

302 

322 

342 

362 

382 

402 

56 

756 

1 

2.1 

756 

4 

402 

421 

441 

461 

481 

501 

520 

55 

755 

2 
3 

4.2 
6-3 

755 

5 

520 

540 

560 

579 

599 

619 

639 

54 

753 

753 

6 

639 

658 

678 

698 

717 

737 

757 

53 

752 

4 

8.4 

752 

7 

757 

776 

796 

816 

835 

855 

874 

S2 

75i 

5 
6 

10.5 
12.6 

751 

8 

874 

894 

914 

933 

953 

972 

992 

5i 

749 

749 

9 

992 

*on 

*03i 

*050 

*°7Q 

*o8g 

3.109 

50 

748 

7 
8 
9 

14.7 
16.8 
18.9 

748 

10 

9.03  109 

128 

148 

167 

187 

206 

226 

49 

747 

747 

11 

226 

245 

265 

284 

303 

323 

342 

48 

745 

745 

12 

342 

361 

381 

400 

420 

439 

458 

47 

744 

744 

13 

45S 

478 

497 

5i6 

535 

555 

574 

46 

742 

on 

742 

14 

574 

593 

613 

632 

651 

670 

690 

45 

741 

1 
2 

2.0 
4.0 

74i 

15 

690 

709 

72S 

747 

766 

786 

805 

44 

740 

740 

16 

805 

824 

843 

862 

881 

901 

920 

43 

738 

3 

6.0 

73S 

17 

920 

939 

958 

977 

996 

*oi5 

*034 

42 

737 

4 

8.0 

737 

18 

9.04  034 

053 

072 

091 

no 

129 

149 

4i 

736 

5 

1 0.0 

736 

19 

149 

168 

187 

206 

225 

244 

262 

40 

734 

6 

7 
8 

12.0 
14.0 
16.0 

734 

20 

262 

281 

300 

319 

338 

357 

376 

39 

733 

733 

21 

376 

395 

414 

433 

452 

471 

490 

38 

73i 

9 

18.0 

731 

22 

490 

508 

527 

546 

56! 

584 

603 

37 

73o 

730 

23 

603 

621 

640 

t>59 

678 

697 

715 

36 

728 

728 

24 

715 

734 

753 

772 

790 

809 

828 

35 

727 

m 

727 

25 

828 

847 

565 

884 

903 

921 

940 

34 

726 

1.9 

3-8 
5-7 
7.6 
9-5 
11.4 

726 

26 

940 

959 

977 

996 

*oi5" 

*o33 

*°52 

33 

724 

724 

27 

9.05  052 

071 

089 

108 

126 

M5 

164 

32 

723 

3 
4 
5 
6 

723 

28 

164 

182 

201 

219 

238 

256 

275 

3i 

721 

721 

29 

275 

293 

312 

330 

'349 

367 

386 

30 

720 

720 

:so 

386 

404 

423 

441 

460 

478 

497 

29 

718 

718 

31 

497 

515 

533 

552 

57o 

589 

607 

28 

7i7 

7 

13-3 

717 

32 

607 

625 

644 

662 

681 

699 

717 

27 

716 

8 

15-2 

716 

33 

717 

736 

754 

772 

79i 

809 

827 

26 

7i4 

9 

17.1 

714 

34 

827 

845 

864 

882 

900 

918 

937 

25 

713 

713 

35 

937 

955 

973 

991 

*oio 

*028 

#046 

24 

711 

7" 

36 

9.06  046 

064 

082 

101 

119 

137 

155 

23 

710 

18 

710 

37 

155 

173 

191 

210 

228 

246 

264 

22 

708 

1.8 

3-6 
5-4 

7-2 

708 

38 

264 

282 

300 

3i8 

336 

354 

372 

21 

707 

1 

707 

39 

372 

390 

408 

426 

445 

463 

481 

20 

705 

2 

3 
4 

705 

in 

481 

499 

517 

535 

553 

57i 

589 

19 

704 

704 

4' 

589 

606 

624 

642 

660 

678 

696 

18 

702 

5 

9.0 

702 

42 

696 

714 

732 

750 

768 

786 

804 

17 

701 

6 

10.8 

701 

43 

804 

821 

839 

857 

875 

893 

911 

16 

699 

7 

12.6 

699 

44 

911 

929 

946 

964 

9S2 

,,l  II  II  1 

*.oiS 

15 

698 

8 
9 

14.4 
16.2 

698 

1' 

9.07  018 

035 

o53 

071 

089 

IO6 

124 

14 

696 

696 

46 

124 

142 

160 

177 

195 

213 

231 

'3 

695 

69! 

47 

231 

248 

266 

284 

301 

319 

337 

12 

693 

693 

48 

337 

354 

372 

390 

407 

425 

44? 

1 1 

692 

17 

692 

\<) 

442 

460 

478 

495 

513 

530 

548 

10 

690 

1 
2 

1-7 

3-4 

690 

:,ii 

548 

566 

583 

601 

618 

636 

653 

9 

689 

689 

51 

653 

671 

688 

706 

723 

741 

758 

8 

687 

3 

5-i 

687 

52 

758 

776 

793 

811 

828 

S46 

863 

7 

686 

4 

6.8 

686 

53 

863 

881 

898 

915 

933 

950 

968 

(. 

684 

5 

8-5 

684 

54 

968 

985 

*""'- 

-;■:■' ''-''  ' 

*Q37 

.,..-,; 

*"72 

5 

683 

6 

7 

10.2 
11.9 

683 

55 

9.08  072 

089 

107 

124 

141 

159 

176 

4 

681 

681 

56 

176 

193 

211 

22S 

245 

262 

280 

3 

6S0 

8 

13.6 

680 

57 

280 

297 

314 

331 

349 

366 

383 

2 

678 

9 

15-3 

678 

58 

383 

400 

418 

435 

-452 

469 

486 

1 

<>77 

677 

59 

1.86 

504 

521 

555 

572 

5S9 

0 

675 

60* 

50" 

40' 

30" 

2D 

10 

0' 

9-99 

P  P 

it:;     263°    *353e 


1,  ( 


61 


IV 

TABLE  OF  THE  LOGARITHMS 

OF  THE 

TRIGONOMETRIC  FUNCTIONS 

FROM  MINUTE  TO  MINUTE 


( 

)° 

*90°  180° 

*27<r 

L  Sin 

d   | 

c  s 

C  T 

L  Tan 

cd 

L  Cot 

L  Cos 

6o 
1 20 

0 

— 00 

6-46  373 

6.76476 

30103 
17609 
1 2494 

9691 

7918 

6694 

5800 

5"5 

4576  - 

4139 

3779 

3476 

3218 

— 00 

30103 
17609 

CO 

0.00  000 

60 

59 

58 

5-31  443 
5-31  443 

5 
5 

31443 
3M43 

6.46  373 
6.76476 

3.53  627 
3-23  524 

M.I  1.  1  MMM 
0.00000 

1  So 

3 

6.94  oS 5 

5-3i  443 

5 

3i  443 

6.94  085 

12494 

3-05  91 5 

O.OOOOO 

57 

240 

4 

7.06  579 

5-31  443 

5 

31  442 

7.06  579 

9691 

2.93  421 

O.OOOOO 

56 

300 

5 

7.16  270 

5  31  443 

5 

31  442 

7.16  270 

7918 

2.S3  730 

O.OO  OOO 

55 

360 

6 

7.24  188 

5-31  443 

5 

3M42 

7.24  188 

6694 

2.75812 

O.OO  OOO 

54 

420 

7.30  882 

5-3i  443 

5 

31442 

7.30  882 

5800 

2.69  11S 

O.OO  OOO 

£3 

4S0 

8 

7.36  682 

5-31  443 

5 

3i  442 

7.36  6S2 

51 1 5 

2.63318 

O.OO  OOO 

52 

5-JO 
600 
660 

9 
10 

1  1 

7-41  797 

5-3i  443 

5 

3i  442 

741  797 

4576 
4139 
3779 

2.5S  203 

O.OO  OOO 

5i 
50 

49 

746  373 

3.3]  443 

5 

31  442 

746  373 

2.53  627 

O.OO  OOO 

7-50  5I2 

5-31  443 

5 

31442 

7-50  5I2 

2.49488 

O.OO  OOO 

720 

12 

7.54291 

5-3i  443 

5 

3i  442 

7-54  29I 

3476 

2-45  709 

0.00000 

48 

7  So 

13 

7-57  707 

5-3i  443 

5 

31442 

7-57  767 

3219 

2.42  233 

0.00000 

47 

S40 

14 

7.60985 

2997 

5-3i  443 

5 

31  442 

7.60  986 

2996 
2803 

2.39014 

O.OO  OOO 

46 

900 

15 

7.63  9S2 

5-3i  443 

5 

31  442 

7.63  982 

2.36018 

O.OO  OOO 

45 

960 

16 

7.66  784 

2633 

2483 
2348 

2227 
2119 
2021 

1930 

1848 

1773 
1704 
1639 

1579 
1524 
1472 
1424  . 

1379 
1336 
1297 
1259 

5-31  443 

5 

31442 

7-66  785 

2633 

2.33  215 

O.OO  OOO 

44 

1020 

17 

7.69417 

5-31  443 

; 

3i  442 

7.69  41S 

2482 

2.30  582 

9.99  999 

43 

10S0 

iS 

7.71  900 

5-31  443 

5 

31  442 

7.71  900 

2348 

2.2S  IOO 

9.99  999 

42 

1 140 
1200 
1260 

19 
2u 

7.74  248 

5-31  443 

5 

31442 

7.74248 

2228 
2119 
2020 

2.25  752 

9.99  999 

4i 
40 

39 

7-76  475 

5-31  443 

5 

31442 

7.76476 

2.23  524 

9-99  999 

7- 7s  594 

5-31443 

5 

3M42 

7-78  595 

2.21  405 

9.99  999 

1320 

22 

7.80615 

5-31  443 

5 

31442 

7.S0615 

I93i 
1848 

2.19385 

9.99  999 

38 

13S0 

23 

7-32  545 

5-31  443 

5 

31442 

7-82  546 

2.17454 

9.99  999 

37 

1440 

24 

7-84  393 

5-31  443 

5 

31  442 

7-84  394 

1773 
1704 
1639 

2.15  606 

9.99  999 

36 

1500 

25 

7.86166 

5-31  443 

5 

31442 

7.86167 

2.13833 

9.99  999 

35 

1560 

26 

7.87  870 

5-31  443 

5 

31442 

7.87871 

2.12  129 

9.99  999 

34 

1620 

7.89  509 

5-3W43 

5 

31442 

7.89  510 

1579 
1524 
1473 
1424 

1379 
1336 
1297 

2.10  490 

9.99  999 

33 

16S0 

28 

7.91  088 

5-31  443 

5 

3i  442 

7.91  089 

2.08  911 

9.99  999 

32 

1740 
1S00 
i860 

29 
30 
31 

7.92  612 

5-31  443 

I 

3i  441 

7.92613 

2.07  3S7 

9-99  99s 

31 
30 

29 

7-94  084 

5-31  443 

- 

31  441 

7-94  086 

-.■•--    ,14 

9-99  99s 

7-95  508 

5-31  443 

- 

3i  441 

7-95  5io 

2.04  490 

9.99  99S 

192c 

32 

7.96887 

5-31  443 

: 

31  441 

7.96  889 

2.03  III 

9-99  998 

2S 

19S0 

33 

7.98  223 

5-31  443 

: 

31  441 

7-gS  225 

2.01  775 

9-99  998 

27 

2040 

34 

7.99  520 

5-31  443 

: 

31  441 

7.99  522 

1259 
1223 
1 190 

2.00  478 

9-99  998 

26 

2100 

35 

8.00  779 

5-31443 

: 

3i  44i 

8.00  781 

1.99  219 

9.99  998 

2^ 

2160 

36 

S.02  002 

1 190 
1158 
1128 
I IOO 
1072 
1046 

1022 

999 

976 

5-3i  443 

5 

31  441 

S.02  004 

1.97996 

9-99  998 

24 

2220 

37 

S.03  192 

5-31  443 

5 

3i  441 

8.03  194 

1159 
112S 

1.96  806 

9-99  997 

23 

22S0 

3* 

8.04  350 

5-31  443 

; 

31  441 

8.04  353 

1.95  647 

9.99  997 

22 

2340 
2400 
2400 

39 
40 

41 

8.05  478 

5-31  443 

5 

31  441 

8.05  481 

I  IOO 

1072 
1047 
1022 
998 

I.94  5I9 

9.99  997 

21 
20 
19 

S.o(,  57S 

5-31  443 

5 

31  441 

8.06  581 

I.93  4I9 

9-99-  )<>7 

8.07  650 

5-31  444 

5 

31440 

8.07  653 

i-92347 

'I.09  997 

252c; 
2580 

42 

43 

8.08  696 

8.09  718 

5-3i  444 
5-31444 

5 

3M40 
31440 

8.08  700 

8.09  722 

1. 91  300 
1.90  27S 

9.99  997 
9.99  997 

iS 

17 

2640 

44 

8.10717 

5-31  444 

5 

31  44" 

8.10  720 

976 
955 
934 

1.S9280 

9.99  996 

16 

270c 

4? 

8. 1 1  693 

5-31  444 

; 

31  440 

8.1 1  696 

1.SS304 

9-99  996 

15 

2760 

46 

8.12  647 

954 
934 

9M 
896 
877 
860 

843 
827 
812 

5-31  444 

; 

31  440 

8.12  651 

r.87349 

9.99  996 

14 

_,-_, 

47 

8.13  581 

5-31  444 

5 

31  44" 

8.13  585 

915 
895 
878 
860 

1S6415 

9.99  996 

13 

•-■--< 

4S 

8.14495 

5-31  444 

: 

3i  44" 

8. 14  500 

1.85  500 

9-99  996 

12 

2940 
3000 

49 

50 

8.15  391 

5-3i  444 

; 

;i  440 

S-I5  395 

[.84  605 

9-99  996 

I  I 

10 

8.16268 

5-31  444 

- 

31  439 

S.l  (.273 

i>3  7=7 

9-99  995 

3060 

51 

8.17  128 

--■}i   444 

5 

31  (3<> 

8-I7I33 

843 

1.S2  S<>7 

9.99  995 

9 

3120 

52 

8.17971 

5-31  444 

: 

31439 

8.17976 

1  32  024 

9.99  995 

8 

3180 

53 

8.18  798 

5-31  444 

: 

31439 

8.18804 

812 

[.8i  196 

9.99  995 

7 

3241 

54 

-  [9610 

797 
782 
769 

755 

5-31  444 

5 

31439 

8.19  616 

797 
769 

1.80384 

9.99  99S 

6 

33"" 

55 

8.20407 

5-3'  444 

5 

(]  );■> 

8.20  |i  | 

[-79  5^7 

9.99  994 

5 

3360 

56 

8.21  189 

5-31  444 

5 

3'  43') 

8.2!  I95 

1.78805 

9.99  994 

4 

342o 

57 

S.21  95S 

5-31  44! 

5 

31  439 

8.21  964 

756 
742 
730 

9.99  994 

3 

:r< 

58 

3.22  71  5 

5-31  445 

; 

;■  tf8 

.>.22   720 

[.77280 

9.99  994 

2 

J54< 
j6a 

59 
60 

3.24  [86 

743 
730 

:-;i  mJ 

I 

3i  438 

3.23  \62 

[.76538 

')•'!« 4 

0 

5-3'  145" 

5 

31  438 

-   24  i«,-j 

1.75  SoS 

9.99993 

|  LCos   d 

L  Col 

c  (I 

L  Tan 

L  Mil 

359 


Hi) 


63 


3600 
3660 
372' 
378° 
3840 

39°° 
39<jo 

4020 

4080 

4140 

4 

4260 

4320 

4380 

4440 

450c 

4560  16 

4620  17 

4680 

4740  19 


8.24  1S6 


4800 

4860 

49 
498c 

5040 

5 
5160 

5220 

528c 

534o 

5400 

5460 

55 

558o 

5640 

5 


■jo 


5760  36 
5S20 
588c 
594o 


6oou 

6000 

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8.24  903 

8.25  609 

8.26  304 
8.26988 

8.27  661 

8.28  324 

8.28977 
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8.30  879 


8.31  495 

8.32  103 

8.32  702 

8.33  292 

8.33  875 

8.34  450 
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8-35  578 
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8.37217 
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8.38  276 
8.38  796 
8.39310 
8.39818 
S.40  320 

8.40  816 

8.41  307 


s-4i  792 


8.42  272 

8.42  746 

8.43  216 
8.43  680 
8-44  139 
8-44  594 
8.45  044 
8-45  489 
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8.46  366 


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5.46  799 

8.47  226 

8.47  650 

8.48  069 
8.48  485 

8.48  896 

8.49  304 

8.49  708 

8.50  108 


8.50  504 


8.50897 

8.51  287 
8.51673 
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8.52  810 

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396 

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8.96  689 


8.96825 


8.96  960 

8.97  095 
8.97  229 

8.97  363 
8.97  496 
s.97  629 
8.97  762 
s.97  894 
8.98026 


8.9S157 


s.98  288 
8.98419 
8.98  549 
8.98  679 
s.gs  808 
8.9S937 
s.99  066 
8.99 194 

8-99  322 


8.99450 


8-99  577 
8.99  704 
8.99  830 
8.99  956 
9.00  082 
9.00  207 
9.00  332 
9.00456 
9.00  581 


9.00  704 

9.00  828 
9.00951 

9.01  074 
9.01  196 
Q.oi  318 
9.01  440 
9.01  561 
9.0 r  682 
9.01  803 


9.01  923 
I,  Cos 


130 
130 
129 
129 
129 
128 
128 
128 
127 

126 
126 
126 
125 
125 
124 
125 
1 2  3 
124 
123 
123 
122 

122 


8.94  I95 


8-94  340 
8.94  485 

8.94  63O 

8-94  773 
8.94917 

8.95  060 
8.95  202 
8-95  344 
8.95  486 


8.95  627 


8-95  767 

8.95  908 

8.96  047 
8.96  187 
8.96  325 
S.96  464 
8.96  602 
8.96  739 
8.96  877 


b.97013 


8.97  150 
8.97  285 
8.97421 

8-97  556 

8.97  691 
8.97825 

8-97  959 

8.98  092 
8.98  225 


8.98358 


8.98  490 
8.98  622 
8.98  753 

8.98  884 
8.99015 

8.99  145 
8.99275 
8.99  405 
8-99  534 


8.99  662 


8-99  79i 
8.99919 
9.00  046 
9.00  1 74 
9.00  301 
9.00427 
9-oo  553 
9.00  679 
9.00  805 


9.00  930 


9-01055 
9.01  179 
9.01  303 
9.01  427 
9-oi  550 
9-OI  673 
9.01  796 

9.01  918 

9.02  040 


9.02  162 


L  Cot 


145 
145 
i45 
143 
144 
i43 
142 

142 
142 
141 
140 
141 

139 
140 

138 
139 
138 
i37 
138 
136 
i37 
i35 
136 
i35 
i35 
i34 
i34 
i33 
i33 
i33 

132 
132 
131 
131 

131 
130 
130 
130 
129 
128 
129 
128 
127 
128 
127 
126 
126 
126 
126 
125 
125 
124 
124 
124 
123 
123 
123 
122 
122 
122 


.05  805 


1.05  660 
1.05  5i5 
1.05  37o 
1.05  227 
1.05  083 
1.04940 
1.04  798 
1.04  656 
1.04  514 


9-99  834 

9-99833 
9.99  832 
9.99  831 
9.99  830 
9.99  829 
9.99  828 
9.99  827 
9.99  825 
9-99  824 


■«H  373 


<)■<)<) s- ; 


1.04233 

1.04092 
I-03  952 
1.03  813 
1.03  675 
1.03  536 
1.03  398 
1.03  261 
1.03  123 


9.99  822 
9.99821 
9.99  820 
9.99819 
9.99817 
9.99  816 
9.99815 
9-99814 
9-99813 


1.02  987 


9-99  3I2 


1.02  850 
1.02  715 
1.02  579 
1.02  444 
1.02  309 
1.02  175 
1.02  041 
1. 01  908 
i-oi  775 


1. 01  64; 


cd 


1.01  510 
1.01  378 
1.01  247 
1.01  116 
1.00985 
1.00  855 
1. 00  725 
i-oo  595 
1. 00  466 


.IK)  33S 


I. OO  209 
I. OO  08l 

o.99  954 
0.99  826 
0.99  699 
o.99  573 
0.99  447 
0.99  321 
0.99  195 


0.99  070 


0.98  945 
0.98  821 
0.98  697 

0.98  573 
0.98  450 
0.98  327 
0.98  204 
0.98  082 
0.97  960 


0.97  838 


9.99  810 
9.99  809 
9.99  808 
9.99  807 
9.99  806 
9.99  804 
9.99  803 
9.99  S02 
9.99  801 


9.99  800 


9.99  79S 
9-99  797 
9.99  796 

9-99  795 
9-99  793 
9.99  792 

9-99  79i 
9.99  790 
9.99  788 


9.99  787 


9.99  786 
9-99  785 
9-99  783 
9.99  782 
9.99  781 
9.99  780 

9-99  778 
9-99  777 
9.99  776 


9-99  775 


9-99  773 
9.99  772 
9-99  77i 

9-99  769 
9.99  768 
9.99  767 
9-99  765 
9.99  764 
9-99  763 


174°     264c 


L  Tan 


9.99  761 


L  Sin 


130 

I 

2.2 

2 

4-3 

3 

6.5 

4 

8.7 

S 

10.8 

6 

13.0 

7 

15.2 

8 

17-3 

9 

19.5 

10 

21.7 

20 

43-3 

(0 

05.0 

40 

86.7 

5° 

108.3 

4-3  4-3 

6.4  6.4 

8.6  8.5 

10.8  10.7 


17.2  17. 1 

19.4  19.2 

21.5  2'- 3 
43.0  42.7 
64.5  64.0 
86.0  85.3 

107.5  t°6.7 


23.5 
47.0 

?  •■  5 
94.0 
'7-5 
136 


6.8 
9.1 
11. 3 
.3.6 
15.9 
18.1 
20.4 
22.7 
45-3 


83.3 
104.2    [Q^;. 


1  :.•-•! 


P     V 


9>-3i 

90.7 

1.4.2! 

II3-3 

132 

i:ti 

2.2 

2.2 

4.4 

4-4 

6.6 

6.6 

8.8 

8.7 

11.0 

10.9 

13.2 

13. 1 

IS. 4 

15.3 

17.O 

17.5 

19.8 

22.0 

21.8 

44.0 

43-7 

60.0 

65.5 

88.0 

87.3 

1IO.O 

109.2 

127 

126 

2.1 

2.1 

4.2 

4.2 

0.4 

6.3 

8.S 

8.4 

10.6 

10.5 

12.7 

.  i.fi 

14.8 

14.7 

16.9 

16.8 

19.0 

18.9 

21.2 

21.0 

42.3 

42.0 

63.  S 

63.0 

84.7 

84.0 

105.0 

122 

121 

2.0 

2.0 

4.1 

4.C 

6.1 

6.0 

8.1 

8.1 

10.2 

10. 1 

12.2 

12. 1 

14. J 

14. 1 

10.3 

16.1 

18.3 

18.2 

20.3 

20.2 

40.7 

40-3 

61.0 

60.5 

81.3 

0.7 

101. 7 

ino.S 

68 


*96°  186°  *276° 


L  Sin   d  L  Tan  c  d   L  Col   J.  ( 


9.01  923 


27 
2- 
29 

30 

31 
32 

33 
34 
35 
36 

37 

39 
W 
41 
42 

43 
44 
4? 
46 

47 
48 
49 
50 

5i 
52 
53 
54 

?: 
56 

57 
58 

■?'> 

80 


9.02  043 

9.02  5211 

9-02  757 
9.1 12  874 

9.02  ()(JT 


9.1 13  [09 


9.03  226 

9.03  342 
9.03  458 

9-C3  574 
9.03  690 
9-03  805 

9.03  920 

9.04  034 
9.04  149 


9.04  262 


9.04  376 
9.04  49° 
9.04  603 

9-04  7I5 
9.04  828 

9.04  940 

9.05  052 
9.05  164 
9.05  275 


120 
120 
120 
119 
11S 
tig 
[18 

[17 
[18 
117 

117 
116 
116 
116 
116 
115 
115 
114 
"5 
113 
114 
114 
113 
112 

"3 
112 
112 
112 
in 
in 


9.05  3S6 


9.05  497 

9.05  607 
9-o5  717 
9-o5  827 
9-05  937 

9.06  046 

9.06155 
9.06  264 

9.06372 


>).<>(>  4V 


9.06  589 
9.06  696 
9.06  804 

9.06  911 

9.07  018 
9.07  124 
9.0723] 

9-Q7  442 
9.07  e  r 


9.02  283 
9.02  4114 
9.02  525 
9.02  645 
9.02  766 

9.02  885 

9.03  005 

')■•'}   242 


9.03  361 


9-03  479 
9-03  597 
9-03  714 
9.03  832 

9.03  948 

9.04  065 
9.04  181 
9.04  297 
9-04  4I3 


9.07  65  5 

9-07  758 
9.07  863 

9.07  968 

9.08  072 
9.08  176 
9.08  280 
9-o8  383 
9.08  486 


in 

no 
no 
no 
no 
109 
109 
cog 

!<>- 
IO9 
IO8 
I07 
IOS 
I07 
I07 
IO6 
I07 
I,, I  1 
[OJ 
IO6 
I05 
I05 
I05 
[OS 
I04 
I04 

"'4 
103 
1  <  »3 
103 


9.04  528 
9.04  643 
9.04  758 
9.04  873 

9.04  9S7 

9.05  101 
9.05  214 
9.05  328 
9.05  441 
9-05  553 


9.05  666 


9-oS  589 

L  Cms 


9.05  778 

9.05  890 

9.06  002 
9.06  113 
9.06  224 
9-o6  335 
9.06  445 
9.06  556 

,,.<>(>  Mid 


9-o6  775 


9.06  885 

9.06  994 

9.07  103 
9.07  211 
9.07  320 
9.07  428 
9.07  536 
9.07643 
<).<>7  7=i 


0.97  838 


9.99  76] 


I  <1 


9.M7S5S 

9.<>7  9*'>4 
9.08071 
9.08177 
9.08  283 
9.08  389 
9-o8  49? 
9.08  600 
9.08  705 
9.08  810 


121 
121 
121 
120 
121 
119 
120 
119 
118 
119 
118 
118 
117 


"7 
116 

116 
116 
115 
115 
H5 
115 
114 
114 
113 
114 

"3 
112 
"3 
112 

112 

112 

in 

1  1  1 

III 

no 

in 

no 

109 

no 

109 

109 

108 

109 

108 

108 

107 

108 

107 

106 

107 

[06 

106 

106 

106 

105 

105 

105 

104 


0.97  717 
0.97  596 

"•97  475 

0.97  355 
0.97  234 
0.97  115 
0.96  995 
0.96  876 
0.96  758 


0.96  639 


0.96  521 
0.96  403 
0.96  286 
0.96  168 
0.96052 
o.95  935 
0.95  819 
0.95  703 
0.95  587 


9.99  760 

9-99  759 

9-99  757 
9.99  756 
9-99  755 
9-99  753 
9-99  752 
9-99  751 
9-99  749 


o.95  41 


0.95  357 
0.95  242 
0.95  127 
0.95013 
0.94  899 
0.94  786 
0.94  672 
o.94  559 
0.94  447 


0.94  334 


0.94222 
0.94  no 
o.93  998 
0.93  887 
0.93  776 
0.93  665 

0.93  555 
0.93  444 
0.93  334 


9-99  74^ 
9-99  747 
9-99  745 
9-99  744 
9-99  742 
9-99  741 
9.99  740 

9-99  738 
9-99  737 
9-99  730 


9-99  734 


9-99  733 
9-99  731 
9-99  730 
9.99  728 

9-99  727 
9.99  726 

9-99  724 
9.99  723 
9.99  721 


9.99  720 


0.93  225 


>*'.»' 4 

L  Cot 


0.93  "5 
0.93  006 
0.92  897 
0.92  789 
0.92  680 
0.92  572 
O.92  464 
0.92  357 
0.92  249 


0.92  1  |- 


0.92  031 
0.91  929 
0.91  823 
O.91  717 
0.91  611 
0.91  505 
0.91  400 
".in  295 
0.91  190 

0.9]  1 186 

I.  Tan 


9.99  718 

9-99  717 
9.99  716 

9-99  7i4 
9-99  713 
9-99  7" 
9-99  7io 
9.99  708 
9-99  707 


9.99  7"5 


9.99  704 
9-99  702 
9.99  701 

9-99  699 
9-99  698 
9.99  696 

9-99  6g5 
9.99  693 

999  '"'J 

9-99  689 
9.99687 
9.99  686 
9.99684 
9.99  68  1 
9.99  681 

9.99  h>" 
9.99678 
9-99  677 

9 

L  Sin 


121 

120 

119 

2.0 

2.0 

2.0 

^4-o 

4.0 

4.0 

6.0 

6.0 

6.0 

8.1 

8.0 

7-9 

IO.I 

10.0 

9.9 

u.i 

12.0 

11.9 

14.1 

14.0 

[3.9 

16.1 

[6.0 

[5.9 

18.2 

18.0 

17-8 

20.2 

20.0 

19.8 

40.3 

40.0 

39-7 

60.5 

60.0 

59-5 

80.7 

80.0 

79-3 

100.S 

1 00.0 

99-2 

117 

116 

115  | 

1 

2.0 

1.9 

1.9 

2 

3-9 

3-9 

3-8 

3 

5-8 

5-8 

5-8 

4 

7.8 

7-7 

7-7 

5 

9.8 

9-7 

9.6 

6 

11. 7 

II.O 

H-5 

7 

13.6 

13-5 

'3-4 

8 

15-6 

15-5 

15-3 

9 

17.6 

17.4 

17.2 

10 

1 Q- 5 

19-3 

tg.2 

20 

39-0 

38.7 

3«-3 

30 

58.5 

58.0 

57-5 

40 

78.0 

77-3 

76-7 

50 

97-5 

96.7 

95-8 

29 

j 

28 

2 

27 

3 

26 

4 

25 

5 

24 

6 

23 

7 

22 

8 

21 

9 

•20 

10 

19 

t8 

20 

30 

17 

40 

50 

113 

1.9 

3-8 
5-6 
7-5 
9-4 
II-3 
13.2 

I5-I 
17.0 
18.8 

37-7 
56.5 
75-3 
94.2 

109 

1.8 
3-6 
5-4 
7-3 
9.1 
10.9 
12.7 
14.5 
[6.4 
18.2 
363 
54-5 
72-7 
90.8 


112 
1.9 

3-7 

5-6 

7-5 

9-3 
11. 2 
I3-I 
14.9 
16.8 
18.7 
37-3 
5(1.11 

74-7 
93-31 

108 

1.8 
3-6 
5-4 
7-2 
9.0 
10.8 
12.(1 
M-4 
16.2 
18.0 
36.0 
54-0 
72.0 
90.0 


P  P 


111 
1.8 

3-7 
5.6 
7-4 
9.2 
11. 1 
13.0 
14.8 
16.6 
18.5 
37-0 
55-5 
74.0 
92.5 


3-9 

5-9 

7-9 

9.8 
n.8 
13-8 
15-7 
17-7 
19.7 
39-3 
59-° 
78.7 
98.3 

114 

1.9 
3-8 
5-7 
76 
9-5 
11 -4 
13-3 
15.2 
17.1 
19.0 
38.0 
57-o 
76.0 
95.0 

110 
1.8 

3-7 
5-5 
7-3 
9-2 

II.O 
12.8 

'4-7 
16.5 
18.3 
36.7 
55-o 
73-3 
91.7 


107 

106 

1.8 

1.8 

3-6 

3-5 

5-4 

5-3 

7-1 

7-i 

8.9 

8.8 

10.7 

10.6 

12.5 

12.4 

U-3 

14.1 

16.0 

15-9 

17.8 

17-7 

35-7 

35-3 

53-5 

53-o 

71-3 

70.7 

S9.2 

s*.3 

L  sin   d   L  Tan  |  c  d  |  L  Cot   L  Cos 


1*  I' 


5»y 


9.08  914 


9.08  692 
9.08  795 

9.08  897 
9.0S  999 

9.09  IOI 
9.09  202 

9.09  304 
9.09  405 

9.09  506 


y.09  606 


9.09  707 

9.09  S07 

9.09  907 

9.10  006 
9.10  106 
9.10  205 
9.10  304 

9.10402 

9.10  501 


9-IQ599 
9.10  697 
9.10795 
9.10  893 

9.10  990 

9. 11  087 
9.11  1S4 
9. 11  2S1 
9-i  1  377 
9. 1 1  474 


9. 1  I 


9.1 1  060 
9.II  761 

9.11  857 
9.II952 
9.12047 

9.12  I42 
9.12  236 
9.12  33I 

9-i2425 


9.12  519 


9.12  612 
9.12  706 
9.12  799 
9.12  892 
9-12985 
9-13078 

9-13  171 
9-13263 
913  355 


9-13  447 


9-r3  539 
9.13  630 
9.13722 

9.13904 
9-13994- 
9.14085 

9-14  175 

9-14  266 


9-I4  35<1 


101 
100 
100 
99 
100 
99 
99 
98 

99 
98 
9S 
98 
98 
97 
97 
97 
97 
96 
97 
96 
96 

95 
96 
95 
95 
95 
94 
95 
94 
94 
93 
94 
93 
93 
93 
93 
93 
92 
92 
92 
92 
91 
92 
91 

91 
90 

91 
90 

91 
90 


9.09  019 
9.09  123 
9.09  227 
9.09  330 
9-t>9  434 
9-09  537 
9.09  640 
9.09  742 
9.09845 


9-Q9  947 


9.10049 
9.10  150 
9.10  252 

9-IQ353 
9.10454 
9-IQ555 
9.10  656 
9-10756 
9-io  856 


9.10  956 


9.11  056 
9-"  x55 
9-H  254 

9-11  353 
9.11  452 
9-"  55i 
9. 1 1  649 

9-"  747 

9-"S45 


943 


9.12  040 
9-12  138 
9-12235 
9.12  332 
9.12  428 
9.12  525 
9.12  621 
9.12  717 
9-12813 


9.12  909 


9.13  004 
9.13  099 
9-13  194 
9.13289 

9-r3  3S4 
9-J3  478 

9-13  573 
9-13667 
9.13  761 


0.91  086 


9^3  854 


L  Cos 


9.13948 
9.14  041 

9- M  134 
9.14227 
9-14320 
9.14412 

9-M  504 
9-14  597 

9.14688 


9-M  780 


LCot 


104 
104 
103 
104 
103 
103 
102 
103 
102 
102 
101 
102 

IOI 

IOI 
IOI 
IOI 

100 

100 

100 

100 

99 

99 

99 

99 

99 

98 


0.90  981 
0.90  877 
0.90  773 
0.90  670 
o  90  566 
0.90  463 
0.90  360 
0.90  258 
0-90  155 
0-90053 


9-99  675 

9.99  <>-  | 

9.99  670 
9.99  669 
9.99  667 

9.99  666 

9-99  664 
9.99  663 
9.99  66 


999  °59 


0.89951 
0.89  850 
0.89  74S 
0.89  647 
0.89  546 
0.89  445 

0.89  344 
0.89  244 
0-89  M4 


9.99658 
9.99  656 
9-99  655 

9-99  653 
9.99651 
9.99  650 
9.99  648  . 
9.99  647   42 
9-99  645 


0.89  044 


0.88  944 
0.88  845 
0.88  746 
0.88  647 
0.8S  548 
0.S8  449 
0.88  351 
0.88  253 
0.881 55 


9-99  64' 


.-'S  u-;- 


0.87  960 
O.87  862 
O.87  765 

0.87  668 
0.87  572 

O.S7  475 

0.87  379 

0.87  2S3 
o.S7  1S7 


0.87  091 


0.S6  996 
0.86  901 
0.86  806 
0.86  711 
0.86616 
0.86  522 
0.86427 
0.S6  333 
q.86  239 


0.86  146 


0.86052 
0.85959 
0.85  866 

0.85  773 
0.85  680 
0.S5  588 
0.85  496 
0.85  403 
Q-85  312 
0.85  220 


172°  262°  *352° 


c  d  I  L  Tan 


9-99  °33 
9.99  632 
9.99  630 
9-99  629 


9-99  625 
9-99  624 
9.99  622 
9.99  620 
9.99  618 
9.99617 
9.99615 
9-99  6l3 
9.99  612 


9.99  610 


9.99  6o3 
9.99  607 
9.99  605 

9-99  6°3 
9.99  601 
9.99  600 
9.99  598 
9.99  596 
9-99  595 


9-99  593 


9.99  591 
9.99  589 

9-99  588 
9.99  5S6 
9-99  5S4 
9.99  582 

9.99  581 
9-99  579 
9-99  577 


9.99  643   40 


9.99  640   38 
9.99  638   37 

9-99  °37  36 
9-99  635  35 
34 
33 
32 
3i 
30 
29 
28 
27 
26 
25 
24 
23 


9-99  5  75 


L 


3«» 


105 

104 

10)5 

I 

1.8 

i-7 

i-7 

2 

3-5 

3-5 

3-4 

3 

5-2 

5-2 

5-2 

4 

7.0 

6.9 

6.9 

5 

8.8 

8.7 

8.6 

6 

10.5 

10.4 

10.3 

7 

12.2 

12.1 

12.0 

8 

14.0 

13-9 

13-7 

9 

15-8 

15.6 

15-4 

10 

17-5 

17-3 

17.2 

20 

35-o 

34-7 

34-3 

30 

52.5 

52.0 

51-5 

40 

70.0 

69-3 

68.7 

5" 

87.5 

86.7 

85-8 

101 

100 

99 

1 

1.7 

i-7 

1.6 

2 

3-4 

3-3 

3-3 

3 

B.o 

5-o 

5-o 

4 

6.7 

6.7 

6.6 

5 

8.4 

8-3 

8.2 

6 

IO.I 

1 0.0 

9.9 

7 

11. 8 

11. 7 

11.6 

8 

1.3-5 

13-3 

132 

9 

15-2 

15-0 

14.8 

10 

16.8 

16.7 

16.5 

20 

33-7 

33-3 

33-o 

30 

SO.  5 

50.0 

49.5 

4" 

67-3 

66.7 

66.0 

50 

84.2 

83-3 

82.5 

97 

96 

95 

1 

1.6 

1.6 

1.6 

2 

3-2 

3-2 

3-2 

3 

4.8 

4.8 

4.8 

4 

6-5 

6.4 

6.3 

5 

8.1 

8.0 

7-9 

6 

9-7 

9.6 

95 

7 

1 1 -3 

1 1.2 

11. 1 

8 

12. 9 

[2.8 

12.7 

9 

14.6 

144 

14.2 

10 

16.2 

[6.0 

15-8 

20 

32.1 

32.0 

3i-7 

30 

48.5 

48.0 

47-5 

40 

64.7 

04.0 

6.3-3 

50 

80.8 

80.0 

79.2 

93 

92 

91 

1 

1.6 

15 

1.5 

2 

3-1 

3-i 

3-o 

3 

4.6 

4.6 

4.6 

4 

6.2 

6.1 

6.1 

5 

7.8 

7-7 

7.6 

6 

9-3 

9.2 

9.1 

7 

10.8 

10.7 

10.6 

8 

12.4 

12.3 

12. 1 

9 

1 4.0 

13-8 

13.6 

10 

15-5 

15-3 

15-2 

20 

31.0 

3"-  7 

30.3 

30 

46.5 

46.0 

45-5 

40 

02.0 

61.3 

50 

77-5 

76.7 

75-8 

102 
i-7 
3-4 

5-i 
6.8 

8-5 
10.2 
11.9 
13-6 
15-3 
17.0 
34-0 
51.0 
68.0 
85.0 

98 

1.6 

3-3 

4.9 

6-5 

8.2 

9.8 

1 1.4 

13-1 

«4-7 

16.3 

32-7 

49.0 

65-3 

81.7 

94 

1.6 
3-i 
4-7 
6-3 

7-8 
9-4 
11.0 
12.5 
14.1 
15-7 
31-3 
47.0 
62.7 
78.3 

90 
i-5 
3-o 
4-5 
6.0 

7-5 
9.0 
10.5 
12.0 
13-5 
15.0 
30.0 
45-0 
60.0 
75.0 


P  P 


*96°  186°  *278c 


L  "-in 


c  d   L  Cot 


L  C 


P  P 


9.14  350 


7 
S 

9 
LO 

11 

12 
13 
14 
1? 
16 

17 
iS 

I.) 

20 

21 

22 
23 
24 
25 

26 

27 

2S 
29 

30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

+  7 
48 
19 

7,(1 

:| 
52 

53 

54- 
55 
56 

57 

80 


9-14445 
9.14  535 
9.14624 

9.1  I  -14 

• 
9.14  891 

9.14980 
9.15069 

,1-  157 


9-15245 


9-15  333 

9.15  421 
9-J5  5o8 

9-I5  596 
9-15683 
9-15  77o 
9-x5  857 

9-15  944 

9.16  030 


.16 


9.16  203 
9.16289 
9-I6  374 
9.16460 
9-l6545 
9.16  631 

9.16  716 
9.16  80 

9> 


II,  vM, 


97O 


9-J7  055 
9-!7i39 

9-17223 

9.17307 
9-17  391 
9-17  474 

9-I7  558 
9.17  (.(i 

M7  7-4 


,.17-07 


9.17890 

9-17  973 

9-18055 

9-I8I37 
9.18  220 
9.18  302 

9.18383 
9.18  465 
9-l8  547 


1  -  f.-j.s 


'/.i  -  7'"/ 
9.18790 

9.18  871 
9.18952 
9.19033 

l.ig  n  j 

9.19  193 
9.19  273 

I  i-,   -  j 
">   I  '' 
1     LC08 


9.14  7S0 


9.14  872 
9.14963 
9-r5  054 

9-15  M5 
9.15236 
9-I5  327 
9-I5  4I7 
9-15  508 

9.15  598 


9-1.5 


9-15  777 
9.15867 
9.15956 
9.16046 
9.16135 
9.16224 
9.16  312 
9.16  401 
9-16489 


9-16577 


9.16  665 

9-16753 

9.16  841 

9.16928 

9.17  016 
9.17  103 
9.17  190 
9.17  277 
9-I7  363 


9-I7  45Q 


9-I7  536 

9.]  7  1)22 

9.17  708 

9- 
9- 

9.17965 

9.18  051 
9.18  136 
9.18  221 


7  794 

.7  880 


9.1s  30(1 


9-18391 
9-I8  475 
9.1S  560 

9.18644 
9.18  728 
9.18  812 
9.18  896 
9.18979 


9.19  '  r 


9.I9  229 
9. 1  9  3 1  2 
9-19  395 
9.I9478 

9.I9643 

9.19  B07 

9  I9  SK9 


88 


0.S5  220 


9.1997' 


0.85  128 
0.85037 
0.84  946 
0.84  855 
0.84  764 
0.84  673 
0.84  583 
0.84  492 
0.84  402 


9-99  574 
9-99  572 
9-99  570 
9.99  56S 
9.99  566 
9-99  56! 
9-99  563 
9-99  56i 
9-99  559 


87 
88 

87 
87 

87 
86 
87 
86 
86 
86 
86 
86 
85 
86 

85 
85 
85 
85 
84 
85 
84 

84 
84 
S4 
-> 
N 
83 
83 
83 
83 
83 

83 
82 
82 
82 
82 
82 


0.8431 


9-99  557 


0.S4  223 
0.84  133 
0.84  044 

0.83  954 
0.83  865 
0.83  776 
0.83  688 
0.83  599 
0.83  511 


9-99  556 
9-99  554 
9-99  552 
9-99  550 

9-99  548 
9.99  546 

9-99  545 
9-99  543 
9-99  54i 


0-83  423 


9-99  539 


0.S3335 
0.83  247 
0.83  159 
0.83072 
0.S2  984 
0.82  897 
0.82  810 
0.82  723 
0.82  637 


0.82  550 


0.82  494 
0.82  378 
0.82  292 
0.82  206 
0.82  120 
0.82  035 
0.81  949 
0.81  864 
0.81  779 


0.81  694 


0.81  609 
0.81  525 
0.8]  440 
0.81  356 
0.81  272 
0.S1  188 
0.S1  104 
0.81  021 
0.80937 


9-99  537 
9-99  535 
9-99  533 
9-99  532 
9-99  530 
9.99  528 
9.99  526 
9-99  524 
9-99  522 


9.99  520 


9.99518 
9-99  517 
9-99  515 
9-99  513 
9-99  5" 
9-99  509 
9-99  507 
9-99  505 
9-99  503 


9.99  501 


O.80  35  1 


o.So  771 

,,.:■>,,  988 
0.80  605 
0.80  522 
0.80  439 
0.80357 
0.80275 
O.80  I93 
O.80  in 


1.  Col 


i7i°   2«r 


L  Tai 

~8F 


9-99  499 
9-99  497 
9-99  495 
9.99  494 
9-99  492 
9.99  490 

9.99488 
9.99  486 
9-99  4S4 


9-99  4s" 
9.99  47S 

9-99  476 

■1.09  474 
0.00  17- 

9.99  47" 

9.99  46S 

0.00  [66 
9-99  I'1' 
9.99  462 


59 
58 

57 
56 
55 
54 
53 
52 
5i 
50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

39 

38 
37 
36 
35 
34 
33 
32 

30 

29 

28 
27 
26 
25 
24 

23 
22 
21 
20 

19 

iS 

17 
16 
15 
14 
13 


92 

91 

I 

1.5 

1.5 

2 

3-i 

3-o 

3 

4.6 

4.6 

4 

6.1 

6.1 

5 

7-7 

7.6 

6 

9-2 

9.1 

7 

10.7 

10.6 

8 

12.3 

12. 1 

9 

13.8 

13.6 

10 

15-3 

15-2 

20 

30.7 

30.3 

30 

46.0 

45-5 

40 

61.3 

60.7 

50 

76.7 

75-8 

89 

88 

1 

i-5 

i-5 

2 

3-0 

*9 

3 

4-4 

4-4 

4 

5-9 

5-9 

5 

74 

7-3 

6 

8-9 

8.8 

7 

10.4 

10.3 

8 

11.9 

n. 7 

9 

13-4 

13.2 

10 

14.8 

U-7 

20 

29.7 

29-3 

30 

44-5 

44.0 

40 

59-3 

58.7 

50 

74-2 

73-3 

86 

85 

1 

i-4 

1.4 

2 

2.9 

2.8 

3 

4-3 

4-2 

4 

5-7 

5-7 

5 

7-2 

7-i 

6 

8.6 

8.5 

7 

10.0 

9-9 

8 

11. 5 

"•3 

9 

12.9 

12. S 

10 

14-3 

14.2 

20 

28.7 

2S.3 

30 

43.0 

42.5 

40 

57-3 

56.7 

50 

71.7 

70.S 

83 

82 

1 

1.4 

i-4 

2 

2.8 

2.7 

3 

4.2 

4-i 

4 

5-5 

5-5 

5 

6.8 

6 

B-3 

S.2 

7 

9.7 

9.9 

8 

11. 1 

[O.9 

9 

12.4 

12.3 

10 

13.S 

13-7 

20 

27-7 

27-3 

30 

41-5 

41.0 

4" 

55-3 

54-7 

5" 

69.2 

68.3 

90 

i-5 
3-o 

4-5 

6.0 

7-5 

9.0 
10.5 
12.0 
13-5 
15.0 
30.0 
45.0 
60.0 
75-o 

87 
i-4 
2.9 
4-4 
5-8 
7-2 
8.7 
10.2 
11.6 
I3-0 

14-5 
29.0 
43-5 
58.0 

72.5 

84 
1.4 
2.8 
4.2 
.5-6 
7-o 
8.4 
9.8 
11. 2 
12.6 
14.0 
28.0 
42.0 
56.0 
70.0 

81 
1-4 
2-7 
4.0 

5-4 
6.8 

S.i 

9-4 
10.8 
12.2 

13-5 

27.0 

4"- 5 
54.0 
67.5 


r    P 


9 


•99      189°    *279c 


L  Sin 


L  Tan     c  d      L  Cot       L  Cos 


V    V 


9-J9  433 


9-J9  513 

9.19592 
9.19  672 

9-I9  75I 
9.19  830 
9.19  909 

9.19  988 
9.20067 

9.20  145 


9.20  223 


9.20  302 
9.20380 
9.2045s 

9-20  535 
9.20  613 
9.20  691 
9.20  768 
9.20  845 
9.20  922 


9-2Q  999 


9.21  076 
9.21  153 
9.21  229 
9.21  306 
9.21  3S2 
9-2I453 

9-2i  534 
9.21  610 
9.21  685 


9.21  701 


9.21 836 

9.21  912 

9.21  987 

9.22  062 

9.22 137 

9.22  211 
9.22  286 
g.22  361 

9-22  435 


5  "9 


9.22  583 
9-22657 
g.22  731 
9.22  805 
9.22  878 

9.22  952 

9.23  025 
9-23098 
9-23  J7i 


9-23  244 


9-23  3I7 
9.23  390 
9.23462 

9-23  535 
9.23  607 
9.23  679 

9-23  752 
9-23  823 
9-23  895 


9.23967 


9.1007.1 


9.20053 
9.20  134 
9.20  216 
9.20  297 
9.20378 
9.20459 
9.20  540 
9.20  621 
9.20  701 


')•-«>  7s- 


9.20  862 

9.20  942 

9.21  022 
9.21  I02 
9.21  182 
9.21  26l 
9-21  341 

9.21  420 
9.21  499 


9-21  578 


9-2i  657 
9.21  736 
9.21  S14 
9.21  893 

9.21  971 

9.22  049 
9.22  127 
9.22  205 

9-22  283 


9-22  36] 


g.22  438 
g.22  516 

9-22  593 
9.22  670 

9.22  747 
9.22  824 

9-22  90I 
9.22977 
9-23  054 


9.23  130 


9-23 


23  206 
9.23  283 
9-23  359 
9-23  435 
9.23  510 
9.23  586 
9.23  661 

9-23  737 
9.23812 


9-23 


9-23  962 
9.24037 
9.24  112 
9.24  186 
9.24  261 
9-24  335 
9.24410 
9.24  4S4 
9-24  558 


9.24  632 


L  Cos 


L  Cot 


cd 


o.s.0 


<»2., 


9-99    V<- 


O.79  947 

0.79  866 
0.79  7S4 
0.79  703 
0.79  622 

0.79541 
0.79  460 
o.79  379 

"■79  -9  1 
O.79  21  S 


9.99  460 

9.99458 
9.99  456 
9.99454 
9.99  452 
9.99  45O 
9.99  448 
9.99  446 
9-99  444 
9.99  442 


0.79  138 
O.79O58 
O.78978 
O.78  898 
O.78818 
O.78  739 
O.78  659 
O.78  580 
O.78  SOI 


9.99  440 
9.99  438 
9.99  436 

9-99  434 
9.99  432 
9.99  429 
9.99  427 
9-99  425 
9-99  423 


0.78  422 


9-99  421 


0.78  343 
0.78  264 
0.78  186 
0.78  107 
0.78  029 
o.77  95i 
o.77  873 
o.77  795 
0.77  717 


Q-77P39 


0.77  562 
0.77  484 
0.77407 

0.77  330 
o.77  253 
0.77176 

0.77  099 
0.77023 
0.76  946 


0.76  870 


0.76  794 
0.76717 
0.76  641 
0.76  565 
0.76490 
0.76414 
0.76339 
0.76  263 
0.76188 


0.76  113 


0.76038 
0.75  9^3 
0.75  888 

0.75814 
o.75  739 
0.75  665 
o.75  590 
O.75  5I0 
o.75  442 


0.75  36S 


L  Tan 


9.99419 
9.99417 
9-99  415 

9-99  413 
9.99  41 1 
9.99  409 
9.99  407 
9.99  404 
9-99  402 


9-99  400 


9.99398 
9.99  396 
9-99  394 
9.99  392 
9.99  390 
9.99  388 

9-99  385 
9-99  383 
9.99381 


9-99  370 


9-99  377 
9-99  375 
9-99  372 

9-99  37o 
9.99  36S 
9.99  366 

9-99  364 
9.99  362 
9-90  359 


9-99  357 


9-99  355 
9-99  353 
9-99  351 
9-99  34S 
9.99  346 
9-99  344 
9-99  342 
9-99  340 
9-99  337 


80 

79 

78 

I 

i-3 

i-3 

1.3 

2 

2-7 

2.6 

2.6 

3 

4.0 

4.0 

3-9 

4 

5-3 

5-3 

5-2 

5 

6.7 

6.6 

6.5 

6 

8.0 

7-9 

7-8 

7 

9-3 

9.2 

9.1 

8 

10.7 

10.5 

'"■4 

9 

12.0 

[1.8 

II. 7 

10 

13-3 

13.2 

13-0 

20 

26.7 

26.3 

26.0 

30 

40.0 

39-5 

39-o 

40 

53-3 

52.7 

52.0 

50 

66.7 

65.8 

65.0 

76 

75 

74 

1 

1-3 

1.2 

1.2 

2 

2-5 

2.5 

2.5 

3 

3-8 

3-8 

3-7 

4 

5-i 

5-o 

4-9 

5 

6.3 

6.2 

6.2 

6 

7-6 

7-5 

7-4 

7 

8.9 

8.8 

8.6 

8 

IO.I 

1 0.0 

9.9 

9 

11.4 

11. 2 

11. 1 

10 

12.7 

12.5 

12.3 

20 

25-3 

25-0 

24.7 

30 

38.0 

37-5 

37-o 

40 

50.7 

50.0 

49-3 

50 

63-3 

62.5 

61.7 

72 

71 

3 

1 

1.2 

1.2 

0.0 

2 

2.4 

2.4 

O.I 

3 

3-6 

3-6 

0.2 

4 

4.8 

4-7 

0.2 

5 

6.0 

5-9 

0.2 

-6 

7.2 

7-i 

0.3 

7 

8-4 

8,3 

0.4 

8 

9.6 

9-5 

0.4 

9 

10.8 

10.6 

0.4 

IO 

12.0 

11.8 

0.5 

20 

24.0 

23-7 

1.0 

30 

36.0 

35-5 

1-5 

40 

48.0 

47-3 

2.1 

50 

60.0 

59-2 

2.5 

3 

3  1 

79 

* 

0 
1 
2 

3 

13.2 
39-5 
65.8 

13-0 
39-0 
65.0 

i-3 

2.6 

3  - 
5-i 
6.4 

9.0 

i". ) 
[1.6 
12.8 

25-7 
38.5 
51-3 
64.2 

73 
1.2 

2.4 

3-6 

4-9 

...1 

7-3 

8-5 

9-7 

11.0 

12.2 

24-3 

36.5 

48.7 

60.8 

2 

0.0 


0.1 
0.2 
0.2 
0.2 
0.3 
0.3 
0.3 
0.7 


9.99 


76 

;i».7 

38.0 
~   63.3 


12.8 

38.5 
64.2 


[2.3 
17.0 


62.5 1 61.7 


L  Sin 


j'    r 


f170°    260°    *350c 


80c 


72 


10c 


100°  190°  *2S0° 


L  Sin 


24039 
24  no 
24181 

24253 
24324 
24  395 
24466 
24536 
24  607 


24677 

24748 
24818 
24888 

24  95  s 

25  028 
25098 
25  168 
25237 
25  307 


26  131 
26  199 
26  267 

26  335 
26403 
26470 

26538 
26  605 
26672 
26,739 

20  Sol, 
26  873 

26  940 
27OO7 

27  073 
27  140 

27  206 

27  273 

27  339 

-7  |0| 
27  Hi 
27  537 
27  D02 

27  668 
-7  734 
27  799 
27864 
27  930 
27  99S 


I  d 


L  Tan 


9-24  032 
9-24  7"'1 

9-24  779 
9-24  853 

9.24  926 

9.25  000 
9.25073 

9.25  146 
9.25  219 
9.25  292 


9-25  365 
9-25  437 
9.25510 
9-25  582 

9-25  655 
9.25  727 
9.25  799 
9.25  871 
9-25  943 
9.26015 


,,.2(,(>Sh 

9.26 158 

9.26  229 
9.26  301 
9.26372 
9.26  443 
9.26  514 

9.26585 
9.26655 
9.26  726 


9-2<>  797 


9.26867 
9.26937 
9.27008 
9.27  078 
9.27  148 
9.27  218 
9.27288 
9-27  357 
9-27427 


9-2  7  496 


9.27  566 
9-27635 
9.27  704 

9-27  773 
9.27  842 

9-27  9II 

9.27  980 

9.28  049 
9.28  117 


9.28  186 


9-28  254 
9.28  323 
9-28  391 
9.28459 
9-28  527 
9.28  595 
9.28  662 
9-28  730 


9.28  865 


L  Cot 


o.7?3..S 


".75  294 
0.75221 
•'•75  M7 
0.75074 
0.75  000 
0.74927 
0.74  854 
O.74781 
0.74  70S 


'-'•74  63J 


0.74  563 

0.74490 
0.74418 

0-74  345 
0.74  273 
0.74  201 
0.74  129 
0.74057 
Q-73  985 


o.73  9M 


0.73  842 
o.73  771 
0.73  699 

0.73  628 
o.73  557 
0.73  486 

o.73  4i5 
o.73  345 
o.73  2  74 


0.73  203 


o.73  133 
0.73  063 
0.72  992 
0.72  922 
0.72  852 
0.72  782 
0.72  712 
0.72  643 
Q-72  573 


0.72  504 


0.72434 
0.72  365 
0.72  296 
0.72  227 
0.72  158 
0.72  089 
0.72  020 
0.71  951 
n.71  .-s; 


"■71 


14 


0.71  740 
"■7i  "77 
0.71  609 

0.71  541 

0.7]  m 

0.71 405 

0.71 338 
0.71 270 
0.71 202 


o-yi  135 

L  Tan 


L  Cos   d 


9-9' 1  33,5_ 


9-99  333 
9.99  33  r 
9.99  32S 
9.99  326 

9-99  324 
9.99  322 

9-99  319 
9-99  317 
9-99  315 


9-99  313 
9.99310 
9.99  308 
9.99  306 
9.99  304 
9-99  301 
9.99  299 
9.99  297 
9.99  294 
9-99  292 


9-99  290 


9.99  200 
9.99  285 
9.99  283 
9.99  281 
9.99  278 
9.99  276 
9.99  274 
9.99  271 
9-99  269 


9-99  267 


9-99  264 
9.99  262 
9.99  260 

9.99  257 
9-99  255 
9.99  252 

9.99  250 
9.99  248 
9-99  245 


9-99  243 


9.99  241 
9.99  238 
9.99  236 

9-99  233 
9.99231 
9.99  229 
9.99  226 
9.99  224 
9-99  221 


9.99  2I9 
9.99217 
9.99  23  1 
9.99  2 1  2 
9.99  20g 
9.99  207 
9.99  204 
9.99  202 
9.99  2<  "  1 
9-99  [97 
g-99  [9lj 
L  Sin 


P  P 


74 

7:-! 

I 

1.2 

1.2 

2 

2.5 

2-4 

3 

3-7 

3-6 

4 

4.9 

A-<> 

S 

6.2 

6.1 

6 

7 

7-4 
S.6 

7-3 
8-5 

8 

9.9 

9-7 

9 

11. 1 

1 1.0 

10 

12.3 

12.2 

20 
30 
40 

50 

24-7 
37-o 
49-3 
61.7 

24-3 
36.5 
48.7 
60.8 

71 

70 

I 

1.2 

1.2 

2 

2.4 

2.3 

3 

3-6 

3-5 

4 

4-7 

4-7 

5 

5-9 

5-8 

6 

7-i 

7.0 

7 

8-3 

8.2 

8 

9-5 

9-3 

9 

10.6 

10.5 

10 

11. 8 

11. 7 

20 

23-7 

23-3 

30 

35-5 

35-o 

40 

47-3 

46.7 

50 

59-2 

58.3 

68 

67 

2 

2.3 

2.2 

3 

3-4 

3-4 

4 

4-5 

4-5 

5 

5-7 

?■<• 

6 

6.8 

6.7 

7 

7-9 

7-8 

8 

9.1 

8.9 

9 

10.2 

1 0.0 

10 

1 1 -3 

1 1.2 

20 

22.7 

22.3 

30 

34-" 

33-5 

40 

45-3 

44  7 

50 

56.7 

55-8 

3 

3 

74 

73 

0 
1 

12.3 
37-o 
61.7 

1  2.2 
36.5 
60.S 

3 

3 

3  . 

71 

70 

69 

11.8 

11. 7 

"•5 

3^-5 

35.0 

34-5 

59.2 

58.3 

57-5  | 

3 

68 

"•3 

34.0 

56.7 


L  Sin 


11°  *lol°     191°     *28! 

L  Tan     ed      L  Cot       L  Cos      d  P    P 


9.28  060 


9.28  125 
9.28  190 
9.28254 

9-28319 
9-28  384 
9.28  448 
9.28  512 
9.28  577 
9.28  641 


9.28  705 


9.28  769 
9-28  833 
9.28  896 
9.28  960 
9.29024 
9.29087 

9-29  150 
9.29214 
9-29  277 


9-29  340 


9.29  403 
9.29  466 
9.29  529 
9.29  591 
9.29  654 
9.29  716 
9.29  779 
9.29  841 
9-29  9°3 


9.29  9(1(1 


9.30028 
9.30  090 
9-30I5I 
9.30  213 
9.30  275 
9-30  336 
9-30  393 
9-30  459 
9.30521 


9-3o  582 


9-30  643 
9.30  704 
9-30  765 
9.30  826 

9.30  887 
9-30  947 

9.31  008 
9.31  068 
9-31  129 


9-3i  it 


9.31  250 
9.31  310 
9-31  37o 
9.31  430 
9.31  490 
9-31  549 
9-31  609 
9.31  669 
9-31  728 


9.28  S65 


9.28933 
9.29  000 
9.29067 
9.29  134 
9.29  201 
9.29  268 

9-29  335 
9.29  402 
9.29  468 
9-29  535 


9.29  601 
9.29  668 
9-29  734 
9.29  800 
9.29  866 
9.29  932 

9.29  998 

9.30  064 
9.30130 


9-3Q  195 


9.30  261 
9.30326 
9-30  391 
9-30  457 
9-30522 
9-30  587 
9.30652 
9-30  7I7 
9.30  782 


9.30  846 


9.30911 
9-30  975 
9.31  040 

9.31  104 
9.31  168 
9-31  233 
9.31  297 
9.31  361 
9-3*425 


9-3i  489 


9-31  552 
9.31  616 
9.31  679 

9-31  743 
9.31  806 
9.31  870 

9-31  933 
9.31  996 
9-32  059 


9.32  122 


9.32185 
9.32  248 
9.32  311 

9-32  373 
9.32436 
9.32  498 
9.32  561 
9.32  623 
9-32685 


9-31  788 


Q-7I  135 


9-99  195 


0.71  067 
0.71  000 
0.70  933 
0.70  866 
0.70  799 
0.70  732 
0.70665 
0.70  598 
0.70  532 


9.99  [92 

9.99  190 
9-99  l87 
9.99  185 
9.99182 
9.99  180 
9.99177 
9-99  175 
9-99  <7- 


0.70465 


>>■_>><)   '7" 


0.70  399 
0.70332 
0.70  266 
0.70200 
0.70  134 
0.70068 
0.70  002 
0.69  936 
0.69  870 


9-99  i67 
9-99  l65 
9.99  162 

9.99  160 
9-99*57 
9-99*55 
9.99152 
9.99150 
9-99  147 


0.69  805 
0.69  739 
0.69  674 
0.69  609 
0-69  543 
0.69478 
0.69413 
0.69  348 
0.69  283 
0.69  21S 


9-99  145 
9.99  142 
9-99  MO 
9-99  137 

9-99  135 
9.99132 
9.99  130 
9.99  127 
9.99  124 
9.99  122 


0-69  154 


9-99  "9 


0.69  089 
0.69025 
0.68  960 
0.68  896 
0.68  832 
0.68  767 
0.68  703 
0.68  639 
0.68  575 


9.99  117 
9.99  114 
9.99  112 
9.99  109 
9.99  106 
9.99  104 
9.99  101 
9-99  099 
9-99  096 


0.68  51 


9-99  093 


0.68  44S 
0.68  384 
0.68321 
0.68  257 
0.68  194 
0.68  130 
0.68  067 
0.68  004 
0.67  941 


9.99091 
9.99  08S 
9.99  086 

9-99  083 
9.99  080 
9.99078 

9-99  075 
9-99  072 
9.99  070 


0.67  878 


9-99  o67 


0.67815 
0.67  752 
0.67  689 
0.67  627 
0.67  564 
0.67  502 
0.67  439 
0.67  377 
0.67315 


9.99  064 
9.99  062 

9-99  o59 

9-99  056 
9.99054 
9.99051 
9-99  048 
9-99  046 
9-99  o43 


9-32  747 


0.67  253 


9.99  040 


I 

65 

64 
1.1 

2 

2.2 

2.1 

3 

3-2 

3-2 

4 

4-3 

4-3 

5 

5-4 

5-3 

6 

6.5 

6.4 

7 

7-6 

7-5 

8 

8.7 

8-5 

9 

9.8 

.,.<■ 

10 

10.8 

'"■7 

20 

21.7 

21.3 

30 

32.5 

32.0 

40 

43-3 

42.7 

5o 

54-2 

53-3 

62 

61 

1 

1.0 

1.0 

2 

2.1 

2.0 

3 

3-i 

3-o 

4 

4-i 

4.1 

5 
6 

5-2 
6.2 

5-i 
6.1 

7 

8 

7-2 

8.3 

7-i 
8.] 

9 

9-3 

9.2 

10 

10.3 

10.2 

20 

20.7 

20.3 

30 

31.0 

30.5 

40 

41-3 

40.7 

50 

51.7 

50.8 

59 

3 

1 

1.0 

0.0 

2 

2.0 

O.I 

3 

3-o 

0.2 

4 

3-9 

0.2 

5 

4.9 

0.2 

6 

5.9 

0.3 

7 

6.9 

0.4 

8 

7-9 

0.4 

9 

s.s 

0.4 

10 

9.8 

0.5 

20 

19.7 

1.0 

30 

29-5 

1.5 

40 

39-3 

2.0 

50 

49.2 

2.5 

1.0 

2.1 

3-2 
4-2 

5-2 

6.3 

7-4 
8.4 
9-4 
10.5 
21.0 
3i-5 
42.0 
52.5 


1.0 
2.0 
3-0 
4.0 

5.0 

6.0 

7.0 

8.0 

9.0 

10.0 

20.0 

30.0 

40.0 
50.0 


0.0 

O.I 
O.I 
O.I 

0.2 
0.2 
0.2 

0.3 
0.3 
0.3 
0.7 

1.0 
i-3 

i-7 


11. 2  11.0  10.8 
33-5  33-o  32-5 
55-8     55-0    54-2 


62 


3 

3 

64 

63 

10.7 

10.5 

32.0 

3i-5 

53-3 

52-5 

10.3 
31-0 

?i-7 


LCos 


LCot 


ed 


L  Tan 


L  Sin 


V     V 


468°    258°    *348° 


78c 


J- 
29 

30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
4'' 
4  7 
48 
49 

50 

5' 
52 
53 

54 

55 

60 


L  sin  ,  (1 


0.31 


9-31  B47 

9.31  966 

9.32  025 
9-32  084 

9.32  261 
9-32  3I9 


9.32  378 


9-32  437 
9.32  195 

9-32  553 
9.32  612 

9-32  72S 
9.32  786 
9.32  S44 
9.32  902 


9-32  960 


9-33  oib 
9-33  075 
9-33  133 
9-33  190 
9.33  248 
9-33  305 
9.33362 
9-33  420 
■'•33  477 


534 


9-33  59' 
9-33  "47 
9-33  704 
9.33  761 
9-33  8i8 
9-33  874 
9-33  931 
9-33  987 
9-34  043 


9-34  100 


9-34  i?'' 
9.34212 
9.34  268 

9-34  324 

9-34  43& 

9-  I  I'M 
9-34  547 
9.34  602 

9-34  6_5j 
9.34713 
9-  t  769 
9.34  824 
9-34  879 


59 
60 

59 

59 

59 
5g 

59 

59 

58 
59 
59 

58 
58 
59 
58 
5S 
5S 
58 
58 
58 
5S 
57 
58 
57 
58 
57 
57 
5S 
57 
57 
57 
56 

57 
57 

57 

56 

57 

56 

56 

57 

56 

56 

56 

56 

56 

56 

55 

56 

55 

56 

55 

56 

55 

55 

55 

55 

55 
55 

5  5 


12  = 

L  Tan  cd   I.  Col 


102« 


9.35 


9.32810 
9-32  872 
9-32  933 
9-32  995 
9-33057 
9-33  "9 
9-33  180 
9-33  242 
9-33  303 


9-33  365 


9-33  426 
9-33  487 
9-33  548 
9.33  609 
9-33  670 
9-33  731 
9-33  792 
9-33  853 
9-33  9I3 


9-33  974 


9-34  034 
9-34  095 
9-34  155 
9.34215 
9.34  276 
9-34  336 
9-34  396 
9-34  45^ 
9-34  5i6 


9-34  576 


9-34  635 
9-34  C'95 
9-34  755 
9.34814 
9-34  S74 
9-34  933 
9-34  992 
9-35  05I 
9-35  in 


9-35  170 


9-35  229 
9-35  288 
9-35  347 
9-35  405 
9-35  464 
9-35  523 
9-35  58i 
9.3S  640 
9-35  698 


9-35  757 


9-35  ^15 
9-35  873 
9-35  931 
9-35  989 

9.3G  163 
9-36  279 


I.  1 


•I 


63 
62 
61 

62 
62 
62 
61 

62 
61 
62 
61 
61 
61 
61 
61 
61 
61 
61 
60 
61 
60 
61 
60 
60 
61 
60 
60 
60 
60 
60 

59 
60 
60 

59 
60 

59 

59 

59 
60 

59 
59 

59 
59 
58 

59 
59 
58 
59 
58 
59 
58 
58 
58 
58 
58 
5* 
58 
58 
58 
5  7 


0.67  253 


0.67  190 
0.67  12S 
0.67  067 
0.67  005 
O.66  943 
0.66881 
0.66  820 
0.66  758 
Q.66  697 


L  Cos   I  d 


9-99  "4" 


0.66  635 


0.66  574 
0.66  513 
0.66452 
0.66  391 
0.66  330 
0.66  269 
0.66  208 
0.66  147 
0.66087 


0.66  026 


0.65  966 
0.65  905 
0.65  845 
0.65  785 
0.65  724 
0.65  664 
0.65  604 
0.65  544 
Q-65  484 


9.99  03S 

9-99  035 
9.99  032 

9.99  030 
9.99027 
9-99  024 
9.99  022 
9.99019 

9-99  old 


9.99OI3 


9.99  on 
9.99  008 
9.99  005 
9.99  002 
9.99  000 
9.98  997 
9.98  994 
9.98  991 
9-98  989 


9.()S  tjS(> 


"-('5  424 


0.65  365 
0.65  305 
0.65  245 
0.65  186 
0.65  126 
0.65  067 
0.65  00S 

"•''4  949 
0.1,4  SS9 


9.98983 
9.98  980 
9.9S  978 

9-98  975 
9.98  972 
9.98  969 
9.98  967 
9.98  964 
9-98  9^i 


9.98  958 


0.64  830 


0.64  771 
0.64-712 
0.64  653 
0.64  595 
0.64  536 
0.64477 
0.64  419 
0.64  360 
0.1,4  30-j 


0.(4  243 


0.64  [85 

0.64  127 
0.64  069 
0.64  01 1 
0.63  953 
0.63  895 
0.63  837 
0.63  779 
0.63  7-1 


9.90  955 

9-98  953 
9.98  950 

9.98  947 
9.98  944 
9.98  941 
9.98  938 
9.9S  936 
9-98  933 


9-98  930 


9.98927 
9.98  924 
9.9S921 
9.98  919 
9.98916 
9.9S913 
9.98  910 
9.98  907 
9.98  904 
9.98  90) 


O.63  664 


LCot     cd     LTan 
347 


9.98  89S 
9.98  896 
9.98  893 
9.98  B90 
9.98  887 
9.9S  884 
9.98  881 
9.9S  878 

9.9SS75 


9.98  872 


56 

55 
54 

53 

5i 
50 

49 

48 
47 
46 
45 
44 
43 
42 
4i 
40 

39 
38 
37 
36 
35 
34 
33 
32 
3i 
30 

29 
28 

27 
26 
25 
24 

23 
22 
21 
20 

r9 

i> 

k, 
15 
14 


*282° 
P  IJ 


63 

|  62 

I 

1.0 

1.0 

2 

2.1 

2.1 

3 

3-2 

3-i 

4 

4-2 

4-i 

5 
6 

5-2 

6.3 

5-2 

6.2 

8 

7-4 

8.4 

7-2 

8-3 

9 

9-4 

9-3 

IO 

10.5 

10.3 

20 

21.0 

20.7 

30 

31-5 

31-0 

40 

42.0 

4i-3 

50 

52.5 

51-7 

60 

59 

1 

1.0 

1.0 

2 

2.0 

2 

.0 

3 

3-o 

3 

.0 

4 

4.0 

3 

•9 

5 

5-o 

4 

<> 

6 

6.0 

5 

') 

7 

7.0 

6 

<) 

8 

8.0 

7 

9 

9 

9.0 

8 

> 

IO 

10.0 

9 

s 

20 

20.0 

19 

- 

30 

30.0 

29 

5 

40 

40.0 

39 

3 

50 

50.0 

49 

2  J 

5  V 

50 

1 

1.0 

2 

1.9 

1.9 

3 

2.8 

2.8 

4 

3-8 

3-7 

5 

4.8 

4-7 

6 

5-7 

5.6 

7 

6.6 

6.5 

S 

7.6 

7-5 

9 

8.6 

8-4 

IO 

9-5 

9-3 

20 

19.0 

18.7 

30 

28.5 

28.0 

[O 

38.0 

37-3 

50 

47-5 

4('-7 

3 

3 

62 

61 

10.3 

10.2 

31.0 
5i-7 

30.5 

50.8 

9.8 
29.5 
49.2 


9.7 
48.3 


18c 


403°  193°  *283° 


L  Sin 


L  Tan 


c  d  |  L  C«>t 


I,  Co 


P  P 


in 


9-35  209 


9-35  263 
9-35  318 

3  9-35*373 

4  9-35  427 

5  9-35  48I 

6  9-35  536 

7  9-35  59° 

8  9-35  644 

9  9-35  69S 


<>o?  7r- 


9.35  S06 

9.35  860 
}  9-35  9*4 

,  9-35  968 

5  9.36022 

6  9.36075 

7  9-36  129 

8  9.36182 

9.36  236 


9.36  2S9 


9-36  342 
9-36  395 
9-36  449 
9.36  502 
9-36  555 
9.36  608 
9.36  660 
9.36  713 
9.36  766 


S19 


9-36^71 
9.36924 
9.36  976 
9.37028 
9-37o8i 
9-37  133 
9-37I85 
9-37  237 
9.37289 


9-37  34' 


37  393 
37  445 
37  497 

37  549 
37  600 
■37652 


,  9-37  703 

48  9-37  755 

49  9.37  806 

50  9-37858 


51  9-3' 

52  9-3- 


53  9-38o 

54  9-38 

55  9-38 

56  9-38 

57  9-38 

58  9-38-. 

59  9-38317 

60  ■).-,>  V' 


062 
113 
i'4 
215 
266 


9-36  336 


9.36  394 
9.36  452 
9-36  509 
9-36  566 
9.36  624 
9.36681 
9-36  738 
9-36  795 
9-36852 
9-36  909 


9.36  966 
9.37023 

9.37  080 

9-37  137 
9-37  193 
9.37250 

9.37  306 
9-37  363 
9-37  419 


9-37  476 


9-37  532 
9.37588 
9-37  644 
9.37  700 
9-37  756 
9.37  812 
9.37  868 
9-37  924 
9-37  98o 


9-38  035 


9.38  091 
9-3§  147 
9.3S  202 

9-38  257 
9-38  3I3 
9.38  36S 

9-38423 

9.3S  479 
9-38  534 


9-3b  5^9 


9.3S  644 
9.3S  699 
9-38  754 
9.38  808 

9.38  863 
9-38918 
9.38972 

9.39  027 
9.39082 


9-39  r36 


9.39  190 
9-39  245 
9.39  299 

9-39  353 
9-39  407 
9.39461 

9-39  515 
9-39  569 
9-39  623 


9-39  677 


0.63  664 


9.90 


0.63  606 
0.63  548 
0.63  491 
0.63  434 
0.63  376 
0.63319 
O.63  262 
0.63  205 
0.63  148 


9.98  869 
9.98  867 
9.98  864 
9.98  861 

().<)>  >=,^ 
9.98855 
9.98  852 
9.98  849 
9.9S  S46 


0.(13  01 1 1 


9-98  843 


0.63  034 
0.62  977 
0.62  920 
0.62  863 
0.62  807 
0.62  750 
0.62  694 
0.62  637 
0.62  581 


9.98  B40 

9.98  837 
9.98  834 
9.98  831 
9.98  828 
9.98  825 
9.98  822 
9.98  819 
9.98  816 


0.62  524 


9-98  8l3 


0.62  468 
0.62  412 
0.62  356 
0.62  300 
0.62  244 
0.62  188 
0.62  132 
0.62  076 
0.62  020 


9.98  810 
9.98  807 
9.98  804 
9.98  801 
9.98  798 
9.98  795 
9.9S  792 
9.98  789 
9.9s  7S6 


o.6i  965 


9-98  783 


0.61  909 
0.61  853 
0.61  798 
0.61  743 
0.61  687 
0.61  632 
0.61  577 
0.61  521 
0.61  466 


9.98  780 
9.9S  777 
9.98  774 
9.9S  771 
9.98  768 

9.9S  762 
9-98  759 


0.61  41 


•'t*  753 


0.61  356 
0.61  301 
0.61  246 
0.61  192 
0.61  137 
0.61  082 
0.61  02S 
0.60  973 
0.60  918 


9.98  750 

9.98  746 
9-98  743 
9.98  740 
9-98  737 
9-98  734 
9.98  731 
9.98  728 
9-98  725 


0.60  864 


9-9S  722 


0.60  810 
0.60  755 
0.60  701 
0.60  647 
0.60  593 
0.60  539 
0.60  4S5 
0.60431 
0.60  377 


9.98  719 
9.98  715 
9.98  712 
9.98  709 
9.98  706 
9.98  703 
'>.< »8  7<  k  1 
9.98  697 
9-98  694 


o.6o  323 


9.98  690 


L  Cos 


L  Cot  I  c  d  L  Tan 


L  Sin 


57 

56 

I 

1.0 

0.9 

2 

1.9 

1.9 

3 

2.8 

2.8 

4 

3-8 

3-7 

5 

4.8 

4-7 

6 

5-7 

5.6 

7 

6.6 

6.5 

8 

7.6 

7-5 

9 

8.6 

8-4 

10 

9-5 

9-3 

20 

19.0 

18.7 

30 

28.5 

28.0 

40 

38.0 

50 

47-5 

46.7 

54 

53 

1 

0.9 

0.9 

2 

1.8 

1.8 

3 

2.7 

2.6 

4 

3-6 

3-5 

5 

4-5 

4-4 

6 

5-4 

5-3 

7 

6.3 

6.2 

8 

7-2 

7,i 

9 

8.1 

B.o 

10 

9.0 

8.8 

20 

18.0 

i  7-7 

30 

27.0 

40 

36.0 

50 

45.0 

44-- 

51 

4 

3 

I 

0.8 

O.I 

0.0 

2 

i-7 

O.I 

O.I 

3 

2.6 

0.2 

0.2 

4 

3-4 

0.3 

0.2 

5 

4.2 

0.3 

0.2 

6 

5-i 

0.4 

7 

6.0 

0.5 

"■4 

8 

0.5 

0.4 

9 

7-6 

0.6 

0.4 

10 

S-5 

0.7 

0.5 

20 

17.0 

i-3 

1.0 

30 

25-5 

2.0 

1.5 

40 

34-" 

2-7 

2.0 

50 

42-5 

3-3 

2-5 

0.9 

1.8 
2.8 

3-7 
4.6 
5-5 
6.4 
7-3 
8.2 

9.2 

18.3 
27-5 
36.7 
45-8 

52 
0.9 

1-7 

2.6 

3-5 
4-3 

5-2 
6.1 

7-8 

8-7 
17-3 
26.0 
34-7 
43-3 


4 

4 

3 

55 

54 

58 

6.9 

6.8 
20.2 

9-7 
29.0 

34.4 
48.1 

47.2 

48.3 

3 

.">7 

9-5 
28.5 

47-5 


3 

3 

56 

55 

9-3 
28.0 
46.7 

9.2 

27.5 

45-8 

54 

9.0 

45-0 


1'  I' 


*166°  256°  *346c 


,r> 


►284° 
P     P 


54 

53 

I 

0.9 

0.9 

2 

1.8 

1.8 

3 

2.7 

2.6 

4 

3-6 

3-5 

5 

4-5 

4-4 

6 

5-4 

5-3 

7 

6.3 

6.2 

8 

7-2 

7-i 

9 

8.1 

8.0 

IO 

q.O 

8.8 

20 

18.0 

17-7 

30 

27.O 

26.5 

40 

36.0 

35-3 

50 

45-o 

44.2 

51 

0.8 

2.6 

3-4 

4.2 

5-i 

6.0 

6.8 

7.6 

8.5 

17.0 

25-5 

34-o 

42.5 


50 

0.8 
1.7 

2.5 
3-3 
4.2 
5.0 

5-8 
6.7 
7-5 
8-3 
16.7 
25.0 
33-3 
41-7 


48 

47 

4 

I 

0.8 

u.S 

O.I 

2 

1.6 

1.6 

O.I 

3 

2.4 

2-4 

0.2 

4 

3-2 

3-i 

0.3 

5 

4.0 

3-9 

0.3 

6 

4.8 

4-7 

0.4 

7 

5-t 

5-5 

0.5 

8 

6.4 

6-3 

0.5 

9 

7-2 

7.0 

0.6 

10 

8.0 

7.8 

0.7 

20 

16.0 

15-7 

1.3 

30 

24.0 

23-5 

2.0 

40 

32.0 

3i-3 

2.7 

50 

40.0 

$9-2 

3.3 

52 

0.9 
i-7 
2.6 
3-5 
4-3 
5-2 
6.1 
6.9 
7.8 

8.7 
17-3 
26.0 
34-7 
43-3 

49 

0.8 
1.6 

2.4 

3-3 

41 

4.9 

5-7 

6-5 

7-4 

8.2 
16.3 
24.5 
32.7 
40.8 

3 

0.0 
0.1 
0.2 
0.2 
0.2 
0.3 
0.4 
0.4 
0.4 

0.5 
1.0 
i-5 
2.0 
2.5 


1 

I 

4 

54 

53 

52 

6.8 

6.6 

6-5 

20.2 

33-8 
47.2 

19.9 
33- J 
46.4 

19-5 

32.5 
45-5 

J 

51 

6.4 
19.1 

3i-9 

44.0 


3 

3 

3 

3 

54 

53 

52 

51 

0 

9.0 

8.8 

8.7 

8.5 

2 
3 

27.0 

26.5 

26.0 

25-5 

45.0 

44.2  43-3 

42.5 

r  r 

15 


L  Sin 


L  Tan    c  d     L  Cot 


L  (  Vis       (1 


P     P 


9-4i  3QO 


9-4i  347 
9-4i  394 
9.41  441 

9.41  438 
9-41  535 
941  582 
9.41  628 
9.41  675 
9.41  722 


9.41  768 


9.41  815 
9.41  S61 

9.41  908 

94i  954 

9.42  001 
9.42  047 
9.42  093 
9.42  140 
942,186 


9.42  23: 


9.42  278 
9.42  324 
9.42  370 
9.42416 
9.42  461 
942  507 
942  553 
942  599 
942  644 


942  690 


942  735 
9.42  781 
9.42  826 
9.42  872 
9.42917 

9.42  962 

9.43  008 
9-43  053 

943  098 


943  143 


943  188 
943  233 
943  278 
943  323 
943  367 
9.43412 

943  457 
943  502 
9.43546 


943  591 
943  635 
9.43  680 
943  724 
943  769 
943  813 
943  857 
943  901 
943  946 
943  990 


944  034 


L  Cos 


942  805 


942  856 

9.42  906 

942  957 

943  007 
943  057 
943  108 
943  158 

9.43  208 
943  258 


943  3o3 
943  358 
943  4o8 
943  458 
943  508 
943  558 
943  607 
943  657 
943  707 
943  756 


943  806 
943  855 
943  9°  5 

943  954 

944  004 
944  053 
9.44  102 

944  151 
9.44  201 
944  250 


944  299 


944  348 
944  397 
944  446 
944  495 
944  544 
944  592 
944  641 
9.44  690 
944  738 


944  787 


944  836 
944  S84 
944  933 

944  981 

945  029 
945  078 
945  126 
945  174 
945  222 


945  271 


945  319 
945  367 
945  415 
945  463 
945  5" 
945  559 
9.45  606 
945  654 
945  702 


945  750 


L  Cot 


Q-57  195 


o.57  144 
0.57094 
0.57043 
0.56993 
0.56943 
0.56  892 

0.56  842 
0.56  792 
0.56742 


9-9*  I'-l 
9.98  491 
',.</-  4- 
9.98  484 
9.98481 
9.9S  477 
9.98  474 
9.98471 
9.98  467 
9-98  464 


0.56  692 


9.98  460 


0.56  642 
0.56  592 
0.56  542 
0.56492 

0.56442 
0.56393 

0.56343 
0.56  293 
0.56  244 


9.98457 

9-98453 
9.98  450 

9.98447 
9-98  443 
9.98  440 

9.98  436 
9-98433 
9.98  429 


Q-56  194 


9-98426 


0.56145 
0.56095 
0.56  046 

o.55  996 
o.55  947 
0.55  898 
0.55  849 
o.55  799 
Q-55  750 


9.98  422 
9.98419 
9.98415 
9.98  412 
9.98  409 
9.98  405 
9.98  402 
9.9S  398 
9-98  395 


Q-55  701 


9-98  391 


o.55  652 
0.55  603 
o.55  554 
o.55  505 
0.55  456 
0.55  408 

o.55  359 
o.55  3io 
0.55262 


9.98  388 
9.98  384 
9.98381 

9-98377 
9-9s  373 
9.98  370 

9.08  366 
9-g8  363 
9-98  359 


0.55  213 


9-98  356 


o-55  164 
0.55  116 
0.55  067 
0.55019 
o.54  97i 
0.54922 

o.54  874 
0.54826 

Q-54  778 


9.98352 
9-98  349 
9-98  345 
9.98  342 
9-98  338 
9-98  334 

9-98  331 
9.98  327 
9-98  324 


o-54  729 


9.98  320 


0.54  681 
0.54633 
0.54  585 
0.54  537 
0.54489 
0.54441 
o.54  394 
0.54  346 
0.54298 


0.54250 


H64c 


cd|  LTan 


9.98317 
9-98313 
9.98  309 

9.98  306 
9.98  302 
9.98  299 
9.98  295 
9.98  291 
9.98  288 


284 


LSin 


51 

50 

I 

0.8 

0.8 

2 

1-7 

1.7 

3 

2.6 

2.5 

4 

34 

3-3 

5 

4.2 

4.2 

6 

5-i 

5.0 

7 

5-8 

8 

6.8 

6.7 

9 

7.6 

7-5 

10 

8.5 

5-3 

20 

17.0 

16.7 

30 

25-5 

25.0 

40 

34-0 

33-3 

50 

42.5 

41.7 

48 

47 

1 

....- 

0.8 

2 

1.6 

1.6 

3 

2.4 

2.4 

4 

3-2 

3-i 

5 

4.0 

3-9 

6 

4.8 

4-7 

7 

5-6 

5-5 

8 

6.4 

6-3 

9 

7-2 

7.0 

10 

8.0 

7-8 

20 

16.0 

15-7 

30 

24.0 

23-5 

40 

32.0 

31-3 

50 

40.0 

39-2 

45 

44 

4 

0.8 

0.7 

O.I 

1-5 

1.5 

O.I 

2.2 

2.2 

0.2 

3-o 

2.9 

0.3 

3-8 

3-7 

0.3 

4-5 

44 

0.4 

5.2 

5-i 

0.5 

6.0 

5-9 

0.5 

6.8 

6.6 

0.6 

7-5 

7-3 

0.7 

15-0 

14.7 

i-3 

22.5 

22.0 

2.0 

30.0 

29-3 

2-7 

37-5 

36.7 

3-3 

49 

0.8 
[.6 

2.4 

3-3 

4-i 

4-9 

5-7 

6.5 

7-4 

8.2 
16.3 
24-5 
32-7 
40.8 

46 
0.8 

i-5 

2-3 

3-i 

3-8 

4.6 

54 

6.1 

6.9 

7-7 
15-3 
23.0 
30.7 
38.3 

3 

0.0 
0.1 
0.2 
0.2 
0.2 
0.3 
0.4 
0.4 
0.4 
0.5 
1.0 
i-5 
2.0 

2-5 


4 

4 

4 

50 

49 

48 

0 

6.2 

6.1 

6.0 

18.8 

18.4 

18.0 

3 
4 

31.2 

30.6 

30.0 

43-8 

42.9 

42.0 

3 

3 

3 

51 

50 

49 

8.5 

8-3 

8.2 

25-5 

25.0 

24.5 

42.5 

41.7 

40.8 

47 

5-9 

7." 

19.4 

41. 1 


48 

5.0 

24.0 
40.0 


P    P 


74c 


7^ 


16^_ 

L  Sin    i     d       L  Tan       c  d  I    L  Cot 


1%3 


^2st;: 


L  Cos 


P    P 


18 
19 
20 
21 
22 
23 
24 
25 
26 

27 

2S 
29 

30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
\6 

47 

48 

49 
50 

;' 
52 
53 
54 
55 

57 
58 

60 


9.44  "34 


9-45  750 


944  O78 

9.44  122 

9-44  166 
9.44210 
9-44  2  53 
9-44  297 
9.44  341 
944  385 
9.44  42S 


9-44  4: 


944  516 

9-44  559 
9.44  602 

9.44  646 
9.44  689 
944  733 
9-44  776 
9.44  Si.) 
9.44  862 


944  9°5 


9-44  948 

9.44  992 
945  035 
9-45  077 
945  120 
945  163 

9.45  206 
9-45  249 
9-45  292 


9-45  334 


9-45  377 
9-45  419 
9.45  462 

9-45  504 
9-45  547 
945  589 
945  632 
9-45  674 
945  7i6 


945  758 


9.45  801 

9-45  843 
945  885 

945  927 

9.45  969 

9.46  01 1 
9.46  053 

9.46  095 
9.46  136 


9.46178 


9.46  '-'.'.I 
9.46  262 
946  303 

9.46  386 
9.46  !-•- 
9.46  469 


44 
44 
44 
43 
44 
44 
44 
43 
44 
44 
43 
43 
44 
43 
44 
43 
43 
43 
43 
43 
44 
43 
42 
43 
43 
43 
43 
43 
42 
43 
42 
43 
42 

43 
42 
43 
42 
42 
42 
43 
42 
42 
42 
42 
42 
42 
42 
41 
42 
42 
42 
4i 
42 
4' 
42 
4i 
42 
4i 
('- 


945  797 
945  84! 
945  892 

9.45  940 
945  987 
946035 

9.46082 

9.46  130 

9.46177 


9.46  224 


9.46271 
9.46319 
9.46  366 
9.46413 
9.46  460 
9.46  507 

946  554 
9.46  601 
9.46  648 


9-46  694 


9.46  741 
9.46  788 
946  S35 
9.46  881 

9.46  928 
946  975 
9.47021 

9.47  068 
9-47  "4 


947  207 
947  253 
947  299 
9-47  346 
9-47  392 
947  43s 
9-47  4S4 
947  530 
947  576 


947  622 


9.47  66S 
9-47  7M 
9.47  760 

9.47  806 
9.47  852 
947  897 
9-47  943 
947  989 
9.4S  035 


,,. 4^  ON) 


I.  c 


9.48  [26 
9.48217 

9 . 1-  262 
9.48  307 
948  353 
9.4S  39S 


47 
48 
47 

48 

47 
48 
47 

48 
47 

47 
47 
48 
47 
47 
47 
47 
47 
47 
47 
46 
47 
47 
47 
46 

47 
47 
46 

47 
46 
46 
47 
46 
46 
47 
46 
46 
46 
46 
46 
46 
46 
46 
4'' 
46 

46 

45 
46 

46 

4'' 
45 
46 
45 
46 
45 
45 
46 
45 
45 
46 
45 


0.54250 


9.9s  284 


0.54  203 
o.54i55 
0.54  108 
0.54060 
0.54013 
o.53  965 
0.53918 
0.53  870 
0.53  823 


9.98  277 
9.98  273 
9.98  270 
9.98  266 
9.98  262 
9.98  259 
9.98  255 
9.98251 


0.53  776 


9.98  24S 


0.53  729 
0.53681 

0.53  634 
0.53587 
0.53  54o 
o.53  493 
o.53  446 
o.53  399 
Q-53  352 


9.98  244 
9.98  240 
9.98  237 
9.98  233 
9.98  229 
9.98  226 
9.98  222 
9.98  218 
9.98  215 


0.53  306 


9.98  211 


0.53259 
0.53  212 
o.53  165 

o.53  "9 
0.53  072 
0.53  025 

0.52979 
0.52  932 
0.52  886 


0.52  640 


0.52  793 
0.52  747 
0.52  701 
0.52  654 
0.52  608 
0.52  562 
0.52  516 
0.52  470 
0.52424 


0.52  378 


0.52  332 
0.52  286 
0.52  240 
0.52  194 
0.52  148 
0.52  103 
0.52057 
0.52  on 
(..51  965 


0.51  920 


0.51  874 
0.51  829 
0.51  783 
0.51  738 
0.51  693 
0.51  647 
0.51  602 
0.51  557 
o-5i  5" 


9.98  207 
9.98  204 
9.98  200 
9.98  196 
9.98  192 
9.98  189 
9.98  185 
9.98  1S1 
9-gg  '77 


9.98174 


9.9S  170 
9.98  166 
9.98  162 
9.9S  159 
9.98  155 
9-98  151 
9.98  147 
9.98  144 
9-98  MQ 


9-9s  136 


9-9»  132 
9.98  129 
9.98  125 
9.98  121 
9.98  117 
9.98  113 
9.98  no 
9.98  106 

i|..|S    Ici'J 


9.98  O98 


.5.   466 


I.  Col 


,1        I.T 


9.98094 
9.98  090 

9.98  0S7 
9.98  083 
9.98  079 
9.98075 
9.98071 
9.98  067 
9.98  063 


L 


11 


48 

47 

I 

0.8 

0.8 

2 

1.6 

1.6 

3 

2.4 

2.4 

4 

3-2 

3-i 

5 

4.0 

3-9 

6 

4.8 

4-7 

7 

5-6 

5-5 

8 

6.4 

6-3 

9 

7-2 

7.0 

10 

8.0 

:■- 

20 

16.0 

15.7 

30 

24.0 

23-5 

40 

32.0 

31-3^. 

50 

40.0 

39-2! 

45 

44 

1 

0.8 

0.7 

2 

i-5 

1-5 

3 

2.2 

2.2 

4 

3-0 

2.9 

5 

3-8 

3-7 

6 

4-5 

4.4 

7 

5-2 

5-i 

8 

6.0 

5-9 

9 

6.8 

6.6 

10 

7-5 

7-3 

20 

15.0 

14.7 

30 

22.5 

22.0 

40 

30.0 

29.3 

5o 

37-5 

3b.  7 

46 

0.8 
i-5 
2-3 
3-i 
3-8 
4-6 
54 
6.1 
6.9 

7-7 
15-3 
23.0 
30.7 

3S.3 

43 

0.7 
1.4 

2.2 

2.9 

3-6 

4-3 

5.0 

5-7 

6.4 

7.2 

1 4- 3 

21-5 

2S.7 

35-8 


42 

41 

4 

0.7 

0.7 

O.I 

1.4 

1.4 

O.I 

2.1 

2.0 

0.2 

2.8 

2.7 

0.3 

3-5 

34 

0.3 

4.2 

4.1 

0.4 

4-9 

4.8 

0.5 

5.6 

5-5 

0.5 

6,3 

6.2 

0.6 

7.0 

6.S 

0.7 

14.0 

13-7 

1.3 

21.0 

20.5 

2.0 

28.0 

27-3 

2-7 

35-0 

34-2 

3-3 

3 
0.0 

0.1 
0.2 
0.2 
0.2 
0.3 
0.4 
0.4 
0.4 

0.5 
1.0 
i-5 
2.0 
2-5 


4 

4 

4 

48 

17 

46 

6.0 

5-9 

5-8 

18.0 

1  7.2 

30.0 

294 

j-.- 

42.0 

41. 1 

40.2 

3 

3 

3 

48 

47 

46 

S.o 

7.8 

7-7 

24.0 

23.5 

40.0 

39-2 

38.3 

45 

5-6 
16.9 

28.1 
394 

3 


7-5 
22.5 


1'      P 


■2S^. 


L  Sin 

9-46  594 

946635 
9.46  676 
9.46717 
9.46758 
9.46  800 
9.46  841 
9.46  882 
9.46923 
9-46  964 


0.47  "..5 


9-47  045 
9.47  086 
9.47127 
9.47  16S 
9.47  209 
9.47  249 
9.47  290 
9-47  330 
9-47  371 


947  4i  1 


947  452 
9-47  492 
947  533 
947  573 
947  613 
947  654 
947  694 
947  734 
947  774 


947  814 


9.47854 
947  894 
947  934 

947  974 
9.48014 
9.48  054 
9.48  094 

948  133 
948  173 
948213 


9.4*5252 
9.48  292 
948  332 
9.4S371 
9.48  41 1 
948  450 
9.4S  490 
948  529 
948  568 


9.48  607 


9.48  647 
9.48  686 
948  725 
9.48  764 
9.48  803 
9.48  842 
9.48  881 
9.48  920 
948  959 
9.48998 


L  Cos 


L  Tan 

94S  534 

9.4S  579 
9.4S  624 
9.4S  669 

948  714 
9.48  759 
9.4S  804 
9.48  849 
9.48  894 
943  939 
948984 


9.49029 
949  073 
9.49  118 

949  l63 
949  207 
9.49252 

949  296 
949  341 

949  385 


949  430 
949  474 
949  519 
949  563 
949  607 
9.49652 
9.49  696 
949  740 
949  784 
949  828 


949  872 


9.49916 
949  960 
9.50004 
9.50  048 
9.50  092 
9.50  136 
9.50  180 
9-50223 
9.50  267 
9-503II 


9-50  355 
9-50  398 
9.50  442 
9.50485 
9-50529 
9-50  572 
9.50616 
9-50659 
9-5Q  703 


9.50  746 


9.50789 
9-50833 

9.50  876 
9.50919 
9.50962 
9-51005 

9.51  048 
9.51092 
9-5II35 


9.51  178 


L  Cot 


c  (1  I    L  Cot 

ie  J  0.51466 

0.51  421 
0.51  376 
0.51  33i 
0.51  286 
0.51  241 
0.51  196 

0.51  151 
0.51  106 
0.51  061 


cd 


0.51  016 


0.50971 
0.50927 
0.50882 
0.50837 
0.50  793 
0.50  748 
0.50  704 
0.50659 
0.50615 


0.50570 


0.50  526 
0.50481 
0.50437 
0.50  393 
0.50  34S 
0.50  304 
0.50  260 
0.50  216 
0.50  172 


0.50  128 


0.50084 
0.50040 
0.49  996 

0.49  952 
0.49  908 
0.49  864 
0.49  820 

o-49  777 
o.49  733 


0.49  689 


0.49  645 
0.49  602 
o-49  558 
0.49515 
0.49471 
0.49  428 

o.49  3S4 
0-49  341 
Q-49  297 


Q-49  254 


0.49  2 1 1 
0.49  167 
0.49124 
0.49081 
0.49  038 
0.48  995 
0.48  952 
0.48  908 
0.48  865 


0.48  822 


162 


L  Tan 


L  Cos 

9.98  060 

9.9S  056 
9.98052 
9.98  043 
9.98  044 
9.98  040 
9.98  036 
9.98032 
9.98  029 
9.9S  023 


<).<)*  (12 


9.98OI7 
9-98  0I3 
9.98  OO9 
9.98  005 
9.98  OOI 

9-97  997 

9-97  993 
9.97  989 
9-97  986 


<>.<>7'^2 


9.97978 
9-97  974 
9.97970 

9-97  966 
9.97  962 
9-97.958 
9-97  954 
9-97  950 
9-97  946 


9-97  942 


9-97  938 
9-97  934 
9-97  930 
9.97926 
9.97922 
9.97918 
9.97914 
9.97910 
9.97906 


<).')7_')"2 


9.97  898 
9.97  894 
9.97  890 
9.97  886 
9.97  8S2 
9.97  S7S 
9.97  874 
9.97  870 
9.()7  Sdi. 


9-97  361 


9.97857 
9-97  853 
9.97  849 

9-97  845 
9.97  84I 

9-97  837 

9-97  833 
9.97  S29 

9-'>7  S-" 


9-97  82I 
L  Sin 


J'     I' 


45 

0.8 
i-5 
2.2 
3-0 
3-3 
4-5 
5-2 
6.0 
6.8 

7-5 
15.0 

22.5 
30.0 
37-5 


0.7 

i-5 
2.2 
2.9 

3-7 
4-4 
5-1 
5-9 
6.6 

7-3 
14-7 
22.0 
29-3 
36.7 


I 

42 

41 

0.7 

2 

14 

i-4 

3 

2.1 

2.0 

4 

2.8 

2-7 

5 

3-5 

3-4 

6 

4.2 

4-i 

7 

4.9 

4.8 

8 

S-6 

5-5 

9 

6-3 

6.2 

10 

7.0 

6.S 

20 

14.0 

13-7 

30 

21.0 

20.5 

40 

28.0 

27-3 

50 

35-o 

34-2 

39 

5 

4 

1 

0.6 

O.I 

O.I 

2 

1.3 

0.2 

O.I 

3 

2.0 

0.2 

0.2 

4 

2.6 

o-3 

0.3 

5 

3-2 

0.4 

0.3 

6 

3-9 

0.5 

0.4 

7 

4.6 

0.6 

0.5 

8 

5-2 

0.7 

0.5 

9 

5-8 

0.8 

0.6 

10 

6-5 

0.8 

0.7 

20 

13.0 

i-7 

i-3 

30 

19-5 

2-5 

2.0 

40 

26.0 

3-3 

2-7 

50 

32-5 

4-2 

3-3 

0.7 
14 

2.2 
2.9 
3-6 

4-3 
5-o 
5-7 
6.4 

7-2 
143 

21.5 

28.7 

35-8 

40 

o-7 
i-3 
2.0 

2-7 

3-3 
[.o 

4-7 
5-3 
6.0 

6.7 
13-3 
20.0 
26.7 
33-3 
3 
0.0 
0.1 
0.2 
0.2 
0.2 
o-3 
0.4 
0.4 
0.4 

0.5 
1.0 

'•? 

2.0 


5 

4 

43 

45 

0 

4-3 

5-6 

2 

12.., 

16.9 

2i-5 

2S.1 

3 

30.1 

39-4 

4 
5 

38.7 

— 

4 

3 

43 

45 

54 

7-5 

16.1 

22.5 

26.9 

37-5 

37-6 

— 

4 

44 

5-5 
16.5 
27-5 

38.5 

3^ 
44 

7-3 
22.0 

3"-  7 


i*    r 


18° 


408°  198°  *288° 


29 
30 

31 
32 
33 
34 
35 
36 
37 
33 
39 
40 
41 
42 
43 
44 
45 
46 
47 
1- 
1  ' 
50 
51 
52 
53 
54 
55 
56 

59 
BO 


LSi] 


9-48998 


949076 

9.49115 

9-49  153 
9.49  192 
9.49231 
9.49  269 
9.49  308 
9-49  347 


949  385 


949  462 

9.49  500 

9-49  539 
9-49  577 
9.49615 

9-49  654 
9.49  692 
9.49  730 


9-49  7(|S 


1 1. 4<  1  806 
9.49  S44 
9.49  882 
9.49920 
949  958 

9.49  996 

9-50  034 
9.50072 

9.50  110 


9-5Q  148 


9.50  185 
9.50223 
9.50  261 
9.50  298 
9-50  336 
9-50  374 

9-50411 
9.50449 
9-5Q  [86 


9-5"523 
9-50561 
9.50  598 
9- 50  635 

9.50673 

9.50  7S4 

9.50  821 
9.50858 
9-5Q  896 

9-50970 

9.51  007 
9-5J  043 

9.5]  117 

9-51  154 
9-51  19' 
9-51  227 
9.;  1  264 


39 

3') 
38 

39 

3'i 

38 

39 

3'i 

38 

39 

33 

38 

39 

38 

38 

39 

38 

33 

38 

38 

38 

38 

38 

38 

38 

38 

38 

38 

38 

37 

38 
38 

37 

38 

38 

37 

38 

37 

37 

38 

37 

37 

38 

37 

37 

37 

37 

37 

38 

37 

37 

37 

36 

37 
37 

37 
3  7 
56 

37 


L  Tun      cd       LCot 


9.51  306 

9-5i  349 
9.51  392 
9-5M35 
9-5i  478 
9.51  520 
9-51  563 


I,.'    I  (Hid 


9-51  64S 
9-51  691 
9-51  734 
9-51  776 
9-51  819 
9.51  861 
9.51  903 
9.51  946 
9.51988 


9-52  03I 


9.52073 
9-52  115 
9-52  157 
9.52  200 
9-52  242 
9-52  284 
9.52  326 
9.52  368 
9.52  410 


9-52  45: 


9-52  494 
9-52  536 
9-52  57S 
9.52  620 
9.52  661 
9.52  703 

9-52  745 
9.52787 
9-52  829 


')■':■-   ^7<> 


9.52912 
9-52  953 
9-52  995 
9-53037 
9-53078 
9-53  120 
9-53  161 
9.53  202 
9-53  24  | 
9-53  285 


I.  (' 


9-53  327 
9-53  368 
9-53  409 

9-53  533 

9-53  574 
9-53  6I5 

9.53650 


9.53  697 


43 
43 

42 
43 
43 
43 
43 
42 
43 
43 
42 
43 
43 
42 

43 
42 

42 

43 
42 
43 
42 
42 
42 
43 
42 

42 

42 

42 

42 

42 

42 

42 

42 

42 

4i 
42 
42 
42 
42 
4i 
42 
4i 
42 
42 
4i 
42 
41 
4i 
42 
4i 
42 
4i 
I' 


0.4S  82: 


0.48  779 
0.48  736 
0.48  694 
0.48  651 
0.4S  608 
0.4S  565 
0.4S  522 
0.4S  4S0 
0.4S437 


0.48  394 


0.48352 
0.48  309 
0.4S  266 
0.4S  224 
0.4S  1S1 
0.4S  139 
0.4S  097 
0.48  054 
0.48  012 


LCos     .1 


9.97  821 


9-97  817 

9.97812 
9.97  808 
9.97  804 
9.97  800 

9.97  796 

9-97  792 
9.97  7S4 


9-97  77'; 


0.47  969 


0.47927 
0.47  8S5 
0.47  843 
0.47  Soo 
0.47  75S 
0.47716 
0.47  674 
0.47  632 
Q-47  590 


9-97  775 
9-97  77' 
9.97  767 

9-97  763 
9-97  759 
9-97  754 
9-97  750 
9-97  746 
9-97  742 


9-97  73S 


0.47  54S 


0.47  506 
0.47  464 

"•47  422 

0.47  3So 
o.47  339 
o.47  297 

0.47255 
0.47213 

0.47  171 


0.47  130 


0.47088 
0.47047 
0.47005 
0.4(1  963 
0.4(1  922 
0.46  880 
0.46  839 
0.46  798 
O46  759 

0.46715 


9-97  734 
9.97  729 
9-97  725 
9.97721 
9-97  717 
9-97  713 
9.97  70S 
9.97  704 
9.97  700 


9.97  696 


9.97691 
9.97  6S7 
9.97  683 
9.97679 
9.97  674 
9.97  670 
9.97  666 
9.97  662 
9-97  657 


9-97  653 


0.46  673 
o.  |o  632 
0.46591 
0.46  5§o 
0.46  508 
0.46  1.67 
o.  )(■  426 
0.46385 
Q-46  344 
0.46  303 


9.97  649 
9-97  645 
9.97  640 

9.97  636 
9.97632 

9.97  628 
9.97  623 
9.97619 
9.97615 


9.97  610 


9.97  606 
9.97  602 

0.07  507 

9-97  593 
0.07  5so 
9-97  584 
0.07  580 
9-07  57'' 
9-97  571  , 
567 


59 

5> 
57 
56 
55 
54 
53 
52 
5i 
50 
49 
4^ 
47 
46 
45 
44 

43 

42 
41 

to 

39 
38 

37 
36 
35 
34 
33 
32 
31 
30 
29 
28 
27 
26 
25 
24 
23 

21 
20 

19 

18 

17 
16 
C5 
M 
13 


r  p 


<1      L  Cot    I  cd.  J  L  T 


F 9-97567  ti 


43 

42 

I 

0.7 

0.7 

2 

1.4 

1.4 

3 

2.2 

2.1 

4 

2.9 

2.8 

5 

3-6 

3-5 

b 

4-3 

4-2 

7 

5-o 

4-9 

8 

5-7 

5.6 

9 

6.4 

6-3 

10 

7-2 

7.0 

20 

M.3 

14.0 

30 

21. s 

21.0 

40 

28.7 

28.0 

50 

35-8 

35-o 

0.6 

i-3 
2.0 
2.6 
3-2 
3-9 
4.6 
5-2 
5-8 

6-5 
13-0 
19-5 
26.0 

32-5 
36 
0.6 
1.2 

1.8 
2.4 

3-0 

3-6 

4.2 

4-8 

5-4 

6.0 

12.0 

18.0 

24.0 

30.0 


41 
0.7 
1.4 
2.0 

2.7 

3-4 
4-i 
4.8 
5-5 
6.2 

6.8 
13-7 
20.5 
27o 
34-2 

37 

0.6 
1.2 

1.8 

2-5 

3-i 

3-7 

4-3 

4-9 

5-6 

6.2 

12.3 

18.5 

24.7 


0.6 

i-3 
1.9 

2-5 

3-8 
4-4 

5-i 

5-7 

6.3 
12.7 
19.0 
25.3 
31.7  I  30.8 


5 

5 

43 

42 

4-3 

4.2 

12.9 

21.5 

21.0 

30.1 

29.4 

38-7 

37-S 

4 

4 

43 

12 

0 

5-4 

5-2 

2 
3 

4 

t6.l 

IS.8 

26.9 

26.2 

37-6 

36.8 

5 
4T 

4.1 
12.3 
20.5 
2S.7 
36.9 


II 

5-1 
'5-4 
25.9 
35.9 


i*   r 


341 


L  Sin 


L  Tan     c  d 


19° 

L  Cot 


81 


199° 


L  Cos 


*289c 

P    r 


9-51  264 


9-51  301 
9-51  333 
9-51374 
9-5M" 
9-51447 
9.51  484 

9.51  520 
9-51  557 

9-5 1  5')3 


9.51 


9.51  666 
9-5 1  702 
9-5i  73S 

9-51  774 
9.51  811 
9-5i  847 
9-51  883 
9-5I9I9 
9-51955 
9-5i99t 


9.52  027 
9-52063 
9.52099 

9-52  135 
9-52  171 
9.52  207 
9.52  242 
9-52278 
9.523U 


9-52385 
9.52421 
9.52456 
9.52492 
9-52  527 
9-52  563 
9-52  598 
9.52634 
9.52  669 


9-52  705 


9-52  74o 
9-52  775 
9.52  811 

9-52  846 
9.52  881 
9-529*6 
9-52  95I 
9-52986 
9.53021 


9-53  056 


9.53092 
9-53  *26 
9-53i6i 

9-53  196 
9-53  231 
9.53  266 

9-53  301 

9-53  336 
9-53  370 


9-52  350 


9-53  405 


9-53  697 


9-53  738 
9-53  779 
9.53  S20 

9-53  861 
9-53  902 
9-53  943 

9-53  984 
9-54  025 
9-54  065 


9.54  106 


9-54  147 
9.54  187 
9.54228 
9.54  269 
9-54  3'") 
9-54  3|o 
9-54  39° 
9-54  431 
9-54  471 


9-54  512 


9-54  552 
9-54  593 
9-54  633 
9-54  673 
9-54  7M 
9-54  754 
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37 

38 

0 

3-i 

3-S 

9.2 

11.4 

3 

15-4 

19.0 

21.6 

26.6 

4 

5 
6 

27.8 

34-2 

33-9 

— 

36 

0.6 

1.2 

1.8 

2-4 

3-o 

3-6 

4.2 

4-8 

5-4 

6.0 

12.0 

18.0 

24.0 

30.0 

31 

0.5 
1.0 
1.6 
2.1 

2.6 

3-i 

3-6 

4-1 

4.6 

5-2 

10.3 

15-5 

20.7 

25.8 

4 

0.1 
0.1 
0.2 
0.3 
o-3 
0.4 
0.5 
o-5 
0.6 
0.7 
i-3 
2.0 

2-7 

3-3 


5 

4 

36 

38 

3-6 

4-8 

10.8 

14.2 

18.0 

23.8 

25.2 

33-2 

324 

— 

II. I 

I8.S 

25.9 

33-3 


4." 
13-9 
23.1 
32-4 


L  Cos 


cl  I  L  Cot  I  c  cl 


L  Tan  I  L  Sin 


1'  V 


458°  248°  *338° 


68° 


84 


202° 


L  Sin 


9-57  3S9 
9.57420 

"■57  4ri 
9.57  482 
9-57  514 

"■57  545 
"•57  57" 
9.57607 

■  1.57  6;^ 


9-57  669 


9.57  700 

"•57  731 
"■5  7  702 

9-57  793 
9.57  824 
9-57  855 
9.57  885 
g.57916 
9-57  947 


9-57  97b 


9.58  008 
9-58039 
9.58070 
9.58  101 
9-58I3I 
9.58  162 

9-58  192 
9.58  223 

<>.;>  2-  ■ 


9-?-s 


9-5t5  3«4 
9-58  34! 
9-58  375 
9.58  406 
9.58436 
9-58  467 
9.58497 
9-58  527 
9-58  557 


■  ,.;-  -—- 


9.58618 

9.58648 
9.58678 
9.58  709 
9-58  739 
9.58  769 

9-58  799 
9.58829 


9.58919 
9-58  949 

9.59009 

,  52  [58 

I.  <ms~ 


L   Tan 

J.'H    |     (^l 


9.60  677 

9.60  714 

9.60  750 

9.60  786 

9.60  823 

9.60  859 

9.60  895 

9.60  93I 

1, .(hi  (,<>; 


9.OI  004 


9.61  040 
9.61  076 
9.6I  112 
9.61  I48 
9.6]  184 
9.61  220 
9.61  256 
9.61  292 
9.6l  328 


9.61  364 


9.61  4OO 
9.61  436 

9.61  472 
9.6I  508 
9.61  544 

9-6i  57" 
9.61  615 
9.61  651 
9.61  687 


9.0! 


9-61  750 
9.61  794 
9.61  830 
9.61  865 
9.61  901 
9.61  936 

9.61  972 

9.62  008 
9.62  043 


9.62  079 


9.62  114 
9.62  150 
9.62  185 
9.62  221 
9.62  251. 
9.62  292 
9.62  327 
9.62  362 
9.62  398 


"■''-'433 


9.62  468 
9.62  504 
9.62  539 

I 
9.62  609 
9.62  645 

9.62  6S0 
9.62  71? 
9.62  750 

"■"-'  7*5 

L  Col 


L  Cot 


"•39  55" 


0.39  323 
0.39  2S6 
0.39  250 
0.39  214 
o-39*77 
0.39  Mi 
0.39  105 
0.39  069 
0.39033 


0.38  996 


0.38  960 
0.38  924 
0.38  888 
0.38  852 
0.38816 
0.38  780 

0.3S  744 
0.38  708 
0.38  672 


0.38  636 


0.3S  600 
0.38  564 
0.38  528 

0.3 S  492 
0.38456 
0.38421 

0.3S3S5 
0.38  349 
0.38  313 


0.3s  27b 


0.3b  242 
0.3S  206 
0.38  170 

0.38  135 
0.38  099 
0.38  064 
0.38028 
0.37  992 
"■57  ";7 


o.37  92' 


0.37  886 
0.37  850 
0.37815 
"■57  77" 
O.37  744 
0.37  708 

0.37  073 
0.37  638 

0.37  56_7 

"■57  532 
"■5  7  496 
"•57  4'" 
O.37426 
"•57  39" 
C37  355 
"■57  320 

O.37  215 

I.  Tan 


L  Cos 
9-96717 


9.90  711 
9.96  706 
9.96  701 
9.96  696 
9.96  691 
9.96  686 
9.96  681 
9.96  676 
9.96  670 


9.96  665 


9.96  660 
9-96655 
9.96  650 
9.96645 
9.96  640 
9.96  634 
9.96  629 
9.96  624 
9.96  619 


9-96614 


9.96  608 
9.96  603 
9.96  598 

9-96  593 
9.96  588 
9.96  582 

9-96  577 
9.96572 

"■"''  rr7 


9-9"  5'' 


9-96  556 
9-96  55I 
9.96  546 

9.96  541 
9-96  535 
9-96  530 

9-96  525 
9.96  520 
9.96514 


9.96  509 


*292° 
P  P 


37 

36  • 

I 

0.6 

0.6 

2 

1.2 

1.2 

3 

1.8 

1.- 

4 

2-5 

2.4 

5 

3-i 

3-o 

6 

3-7 

3-6 

7 

4-3 

4.2 

8 

4-9 

4.8 

9 

5-6 

5-4 

10 

6.2 

6.0 

20 

12.3 

12.0 

30 

18.5 

18.0 

40 

24.7 

24.0 

50 

30.8 

30.0 

32 

31 

1 

0.5 

0.5 

2 

1.1 

1.0 

3 

1.6 

1.6 

4 

2.1 

2.1 

5 

2.7 

2.6 

6 

3-2 

3-1 

7 

3-7 

3-6 

8 

4-3 

4.1 

9 

4.8 

4.6 

TO 

5-3 

5-2 

20 

10.7 

10.3 

3D 

16.0 

15-5 

40 

21.3 

20.7 

5" 

26.7 

25.8 

29 

6 

1 

0.5 

O.I 

2 

1.0 

0.2 

3 

i-4 

0.3 

4 

1.9 

0.4 

5 

2.4 

o-5 

6 

2-9 

0.6 

7 

3-4 

0.7 

8 

3-9 

0.8 

9 

4-4 

0.9 

10 

4-8 

1.0 

20 

9-7 

2.0 

30 

14-5 

3-o 

40 

19-3 

4.0 

50 

24.2 

5-0 

35 


2-3 

2.9 

3-5 
4-1 
4-7 

5-2 
5.8 

II. 7 
17.5 

23-3 
29.2 

30 

0.5 

1.0 

i-5 

2.0 

2.5 

3-0 

3-5 

4.0 

4-5 

5.0 

10.0 

15.0 

20.0 

25.0 

5 
0.1 
0.2 
0.2 

o-3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.8 
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2-5 
3-3 
4.2 


36 

3-o 
9.0 
15-0 
21.0 
27.0 
33-o 


35 

2.9 
8.8 
[4.6 
21  '.4 
26.2 
32.] 


37 

3  7 

25.9 

33-3 


36 

3-6 
[O.S 

IS... 


35 

3-5 
10.5 
17-5 


25.2  24.5 
32.4  5 '-5 


P   1' 


23° 


88 


'113°    203°    *2<)3° 


L  Sin 


L  Tan     cd      L  Cot       L  Cos 


1'     I' 


)-59 


:S3 


9-^2  785 


9.59218 
9-59247 
9.59277 

9-59  307 
9-59  336 
9.59  366 

9-59  396 
9-59  425 
9-59  455 


9-59  484 


9-59  5M 
9-59  543 
9-59  573 
9.59  602 
9-59632 
9.59  661 
9.59  690 
9-59  720 
9-59  749 


w-50 


9-59  808 
9-59  837 
9.59  866 

9-59  895 
9-59  924 
9-59  954 

9-59  983 
9.60012 

9.60041 


9.  (.0099 
9.60  128 
9-60157 
9.60186 
9.60  215 
9.60  244 
9.60  273 
9.60  302 
9-6o33i 


9.60  359 


9.60388 
9.60417 
9.60  446 
9.60  474 
9.60  503 
9.60  532 
9.60  561 
9.60  5S9 
9.60618 


9.60  646 
9-60675 
9.60  704 
9.60  732 
9.60  761 
9.60  789 
9.60818 
9.60  846 
9.60  875 
9.60  903 


9.60931 


30  I  9.62  820 
29  9.62855 
3°  9.62  890 
3  9.62  926 
29  9.62  961 
3°  9.62  996 
iO    , 

9-63031 
9.63066 
9.63  101 


(j.f.3  135 


9.63  170 
9.63  205 
9.63  240 

9-63  275 
9-63310 
9-63  345 

9-63  379 
9.63414 
9-63  449 


9-63  484 


9-63  519 
9-63  553 
9.63  588 

9.63  623 
9.63657 
9.63  692 
9.63  726 
9.63  761 
9.63  796 


9.63  S65 
9.63  899 
9-63  934 

9.63  968 

9.64  003 
9.64037 
9.64  072 
9.64  106 
9-64  Mo 


9-64I75 


9.64  209 
9.64  243 
9.64278 
9.64  312 
9.64  346 
9.64  381 
9.64415 
9.64  449 
9.64483 


9-64  5I7 


■64  552 
.64  586 
.64  620 
.64  654 
.64  688 
.64  722 
■64  756 
64  790 
.64  824 


(,4  >;S 


0.3; 


9-9°  403 


0.37  ibo 
0-37  145 
0.37  no 
0.37074 
0.37039 
0.37004 

O.36  969 
0.36  934 
0.36  899 


9.96  397 
9.96  392 
9.96387 
9.96  381 
9.96376 
9.96  370 

9-96  365 
9.96  360 

<,.<)(.  354 


0.36  865 


9-96  349 


0.36  830 
0.36  795 
0.36  760 
0.36  725 
0.36  690 
0.36  655 
0.36621 
0.36  586 
0.36551 


9-96  343 
9-96  338 
9-96  333 
9.96327 
9.96322 
9.96316 

9-96311 
9-96  305 
9.96  300 


0.36  516 


9.96294 


0.36481 
0.36  447 
0.36412 

0.36  377 
0.36  343 
0.36  308 
0.36  274 
0.36  239 
0.36  204 


9.96  289 
9.96  284 
9.96  278 
9.96  273 
9.96  267 
9.96  262 
9.96  256 
9.96251 
9-96  245 


036  170 


0.36135 
0.36  101 
0.36  066 
0.36032 
o.35  997 
o.35  963 
0.35  928 
o.35  894 
0.35  860 


9-9"  240 


9.96  234 
9.96  229 
9.96  223 
9.96  218 
9.96  212 
9.96  207 
9.96  201 
9.96  196 
9.96  190 


0.35825 


9-96  185 


o-35  79i 
o-35  757 
0.35  722 
0.35  688 
0.35654 
0.35  619 

o.35  585 
o.35  55i 
0.35  5i7 


9.96  179 
9.90174 
9.96  168 
9.96  162 
9.96157 
9-96151 
9.96  146 
9.96  140 
9-96  135 


o.35  483 


9-96129 


0.35  448 
o.35  4i4 
0.35  380 
0.35  346 
0.35  312 
0.35  278 

0.35  244 
0.35  210 
Q-35  176 


9.96123 
9.96  118 
9.96  112 
9.96  107 
9.96  101 
9.96095 
9.96  090 
9.96084 
9.96  079 


0.35  14: 


9.96073 


36 

35 

0.6 

0.6 

1.2 

1.2 

1.8 

1.8 

24 

2.3 

3-o 

2.9 

3-6 

3-5 

4.2 

4-i 

4.8 

4-7 

5-4 

5-2 

6.0 

5-8 

12.0 

11. 7 

18.0 

17-5 

24.0 

23-3 

30.0 

29.2 

30 

29 

0.5 

0.5 

1.0 

1.0 

i-5 

1.4 

2.0 

1.9 

2.5 

2.4 

3-0 

2.9 

3-5 

34 

4.0 

3-9 

4-5 

4-4 

5-o 

4.8 

1 0.0 

9-7 

15-0 

14-5 

20.0 

19-3 

25.0 

24.2 

34 

0.6 
1.1 

1-7 

2-3 

2.8 

3-4 

4.0 

4-5 

5-i 

5-7 

U.3 

17.0 

22.7 

28.3 

28 

0.5 

0.9 

i-4 

1.9 

2-3 
2.8 

3-3 
3-7 
4.2 

4-7 
9-3 
14.0 

18.7 
23-3 


I 

O.I 

O.I 

2 

0.2 

0.2 

3 

0.3 

0.2 

4 

0.4 

0.3 

fi 

0.5 

0.4 

6 

0.6 

0.5 

7 

0.7 

0.6 

a 

0.8 

0.7 

9 

0.9 

0.8 

10 

1.0 

0.8 

20 

2.0 

i-7 

30 

3-o 

2-5 

40 

4.0 

3-3 

50 

5-o 

4.2 

6 

6 

36 

35 

3-o 

2-9 

9.0 

8.8 

15-0 

14.6 

21.0 

20.4 

27.0 

26.2 

33-o 

32.1 

34 

2.8 
8-5 
14.2 
19.8 

25-5 

31-2 


5 

35 

0 

3-5 

10.5 

3 
4 

5 

17-5 

24-5 
3 '-5 

34 

3-4 
10.2 
17.0 

23.8 
30.6 


L  Cos 


L  Cot    I  c  cl 


L  Tan 


LSin    I  d 


I'     P 


156°     240°    *336c 


66° 


24° 


*1U°  204°  *294° 


L  Sin 


93 


9.60960 

9.60  9S8 

9.61  016 
9.6]  04! 

.,."1  <>-} 
9.61  101 
9.61  129 
9.61  158 

<).<>!  IS(, 


9.(1 1  2  14 


9.6]  242 

9.6I  2  70 

9.6I  298 

9.6I  326 

9-6i  354 
9.61382 

9.61  411 
9.61  438 
9.61  466 


9.61494 


9.61  522 
9.61  550 
9.61  578 
9.61  606 
9.61  634 
9.61  662 
9.61  689 
9.61  717 
Q-6i  745 


9-<->i  773 


9.61  000 
9.61  828 
9.61  856 
9.61  883 
9.61  911 
9.61  939 
9.61  966 

9.61  994 

9.62  021 


•).<>-  <  >  4<i 


9.62  076 
9.62  104 
9.62  131 
9.62  159 
9.62  186 
9.62  214 
9.62  241 
9.62  268 
9.62  'J'*'1 


9.62  323 


9.62  350 

9.62  377 
9.62  405 

9.62  459 
9.62  486 
9-62513 

9.62  S')S 


L  Tan    ;  e  d  J    L  Cot 


'<-"4  -^ 


9.64  892 
9.64  926 
9.64  960 

9.64  994 

9.65  028 
9.65  062 
9.65  096 
9.65  130 
9.0?  i<>4 


9.65197 


9-65  231 
9.65  265 
9.65  299 

9-65  333 
9.65  366 
9.65  400 

9-65  434 
9.65  467 
9-^5  501 


9-65  535 


9.65  568 
9.65  602 
9.65  636 
9.65  669 
9-65  703 
9-65  736 
9.65  770 
9.65  803 
9-65  837 


9.65  870 


9.05  904 
9-65  937 
9.65971 

9.66  004 
9.66  038 
9.66071 
9.66  104 
9.66  138 
9.66  171 


().()()  -j<>4 


9.66238 
9.66  271 
9.66  304 

9-66  337 
9.66  371 
9.66  404 
9.66437 
9.66  470 
9.66  503 


9.66  537 


9.66  570 
9.66  636 

9.66  702 

9.66  735 
9.66  768 
9.66  801 


o.35  142 


0.35  108 
0.35  074 

0.35  040 
0.35  006 
0.34972 
0.34  938 
0.34904 
0.34  870 
0.34  836 


0.34  *'>;i 


0.34  769 
o.34  735 
0.34  701 
0.34  667 
o.34  634 
0.34  600 

0.34  566 
0-34  533 
Q-34  499 
0-34  465 


0.34  432 
o.34  398 
o.34  364 

o.34  33i 
0.34297 
0.34  264 
0.34  230 
Q-34  197 
Q-34  163 


0.34  130 


LCos  I  d 


9-96  073 


9.96067 
9.96  062 
9.96056 
9.96050 
9.96  045 
9.96  039 
9.96  034 
9.96028 
9.96  022 


().()(>  01 


9.96  on 
9.96  005 
9.96  000 

9-95  994 
9.95  9S8 
9.95  982 

9-95  977 
9-95  971 
9-95  965 


9-95  960 


9-95  954 
9-95  94 S 
9-95  942 
9-95  937 
9-95  93i 
9-95  925 
9.95  920 
9-95  9*4 
9-95  9oS 


0.34  096 
0.34  063 
0.34029 

0.33  996 
0.33  962 
o.33  929 
0.33  S96 
0.33  862 
Q-33  829 


o-33  796 


0.33  762 
o.33  729 
0.33  696 

0.33  663 
0.33  629 
o.33  596 
o.33  563 
Q-33  530 

0.33  (■»: 
0.33  41 .3 


0.33  430 

o.33  397 
o.33  364 
0.33  331 
0.33  298 
0.33  265 
0.33232 
o.33  199 
n.33  I,,(l 


0.33  133 


9-95  90- 


9-95  897 
9-95  891 
9.95  885 

9-95  879 
9-95  873 
9.95  868 

9.95  862 
9.95  856 
9-95  850 


9-95  844 


9-95  839 
9-95  833 
9.95  827 

9.95  821 
9.95815 
9.95  810 
9.95  S04 

9-95  792 


<>.<)?  :-'> 


9.95  780 
9-95  775 
9.95  76g 

9-95  763 
9-95  ":: 
9-95  751 
9-95  74; 
9-95  739 
9-95  733 


9.  .15 


P  1' 


34 

I 

0.6 

2 

1.1 

3 

1.7 

4 

2-3 

5 

2.8 

6 

3-4 

7 

4.0 

8 

4-5 

9 

5-i 

10 

5-7 

20 

IX-3 

30 

17.0 

40 

22.7 

50 

28.3 

33 

0.6 
1.1 
1.6 
2.2 
2.8 
3-3 
3-8 
4-4 
5-o 

5-5 
n.o 
16.5 
22.0 

27-5 


29 

28 

I 

o-5 

0.5 

2 

1.0 

0.9 

3 

i-4 

i-4 

4 

1.9 

1.9 

5 

2.4 

2-3 

6 

2.9 

2.8 

7 

3-4 

3-3 

8 

3-9 

3-7 

9 

4.4 

4.2 

10 

4.8 

4-7 

20 

9-7 

9-3 

30 

14-5 

14.0 

40 

19-3 

18.7 

50 

24.2 

23-3 

0.4 
0.9 

i-4 
1.8 

2.2 
2-7 
3-2 
3-6 
4.0 

4-5 
9.0 
13-5 
18.0 

22.5 


6 

I 

O.I 

2 

0.2 

3 

0.3 

4 

0.4 

5 
6 

o-5 
0.6 

7 
8 

0.7 
0.8 

9 

0.9 

10 

1.0 

20 

2.0 

30 

3-o 

40 

4.0 

5° 

5.0 

0 

0.1 
0.2 
0.2 


0.6 
0.7 
0.8 

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6 

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34 

33 

2.8 

2.S 

8-5 

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14.2 

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9.62  595 

27 

9.66  867 

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0.33  133 

9.95  728 

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9.62  622 

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9.62  649 

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9.95716 

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9.62  676 
9-62  703 

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9.66  966 
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9.95  710 
9.95  704 

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0.32  968 

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9.63  159 

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9.95  603 

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9.64  647 
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9.64  826 
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9.O4  953 


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9.65  003 
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9.69  010 
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9.69  074 
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9.69  170 
9.69  202 
9.69  234 
9.69  266 
9.69  298 
9.69  329 
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9.69  584 
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9.69  679 
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9.69  868 
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9.70  121 
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9.66  221 
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9.66270 
9.66  295 
9.66  319 
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9.66  465 
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9.66  537 
9.66  562 
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9.60  634 
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9.66  706 
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9.66  779 
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9.66  827 
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9.66  922 


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9-67  161 


9.70  748 
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9-70  935 
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9.72  201 
9.72  231 


9.72  262 


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9-72415 
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9.72  506 
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9.94  988 


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9.94  982 
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9.94  904 

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0.28  630 
0.28  599 
0.28  569 
0.28  538 
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9.94  852 
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9.94  832 
9.94  826 
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9.94  806 
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0.28  321 
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0.28  137 
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9.94  720 
9.94  714 
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9.94  694 
9.94  687 
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9.94  674 
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9.94  660 


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0.27  646 
0.27  616 
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9-94  654 
9-94  647 
9.94  640 

9-94  634 
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0.4 

4 

0.5 

5 

0.6 

6 

0.7 

7 

0.8 

8 

0.9 

9 

1.0 

10 

1.2 

20 

2-3 

30 

3-5 

40 

4-7 

50 

5-8 

O.I 

0.2 

0.3 
0.4 

0.5 
0.6 
0.7 

0.8 
0.9 
1.0 
2.0 
3.0 
4.0 
5-o 


7 

6 

30 

31 

0 

2.1 

2.6 

6.4 

7-8 

3 

4 

12.9 

18.1 

19-3 

23.2 

6 

23.6 

28.4 

7 

27.9 

30 

2.5 

- 

12.5 

17-5 

22.5 


0.27433 


''■'»4  5J23 


L  Cos 


L  Cot      c  d     L  Tan 


L  Sin 


P    P 


452°     242c 


s332 


62 


90 


23c 


418°  208°  *298° 


i3 
14 
15 
16 

17 
18 
19 
20 

21 
22 
23 

-4 
25 
26 

27 
28 

29 

30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

41 
42 
43 
44 
45 
46 

47 
48 
49 
50 

51 
52 
53 
54 
55 
56 
'-- 
58 

60 


L  Sin 


Q.67  i6i 


9.67  [85 

9.67  20S 
9.67  232 
9.67  256 
9.67  280 
9.67  303 
9.67327 
9-^7  350 
9-67  374 


9  67  39S 


9.67  4-1 
9-67  445 

9.67  46S 

9.67  492 
9-67  5I5 
9-67  539 
9-67  562 
9.67  586 
9.67  609 


9-67633 


9.67656 
9.67  680 
9.67  703 
9.67  726 
9.67  750 
9-67  773 
9.67  796 
9.67  820 
9.67  843 


9.67  890 
9.67913 
9.67  936 

9-67  959 

9.67  982 

9.68  006 
9.68  029 
9.68  052 
9.68  075 


9.68  328 


9-68351 
9.68  374 
9.68  397 
9.68  420 
9.68  443 
9.68  466 
9.68  489 

! 


L  Tan  |  c  d  |  L  Cot   L  <  !oa 


9-72  56: 


9.72  59S 
9.72  628 
9.72  659 
9.72  6S9 
9.72  720 
9-72  750 
9.72  780 
9.72  811 
9.72  841 


9.72  872 


9.72  902 
9.72932 
9.72963 

9-72  993 
9-73023 
9-73  054 
9.73084 
9-73  114 
9-73  144 


9-73  175 


L  Cos  I    (1 
*I51°     I'M' 


9-73205 
9-73  235 
9-73  265 
9-73  295 
9  73  326 
9-73  356 
9-73  386 
9.73416 
9-73  446 


•73  47<> 


9-73  507 
9-73  537 
9-73  567 

9-73  597 
9.73627 
9-73  657 
9.73687 
9-73  717 
9-73  747 


9-73  777 


9.73  807 
9-73  837 
9-73  867 
9-73  897 
9-73  927 
9-73  957 

9-73  987 
9.74017 

9.74047 


9-74Q77 


9.74  107 
9-74  137 
9.74  1 66 

9.74  [96 

9.74  226 
9.74256 
9.74  286 
9.74316 
9-74  345 


)-74  375 


30 
3i 
30 

31 
30 
30 

3i 
30 
3i 
30 
30 
3i 
30 
30 
3i 
30 
30 
SO 
31 
30 
30 
30 
30 

31 
30 
30 
30 
30 
30 
31 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
29 
30 
30 
3o 
30 
30 
29 
30 


•27  433 


0.27402 
0.27  372 
0.27341 
0.27  311 
0.27  280 
0.27  250 
0.27  220 
0.27  189 
Q-27  159 


0.27  128 


0.27  098 
0.27  068 
0.27  037 
0.27007 
0.26  977 
0.26946 
0.26916 
0.26  886 
0.26856 


0.26825 


0.26  795 
0.26  765 
0.26  735 
0.26  705 
0.26  674 
0.26  644 
0.26614 
0.26  584 
0-26554 


9-94  593 


9-94  587 
9.94  580 
9-94  573 
9-94  567 
9.94  560 
9-94  553 
9.94  546 
9.94  540 
9-94  533 


9-94  526 


9.94  519 
9-94  513 
9.94  506 

9-94  499 
9.94  492 
9.94485 

9-94  479 
9.94  472 
9-94  465 


9-94  458 


0.26  524 


0.2')  493 
0.26463 
0.26433 
0.26  403 
0.26373 
0.26  343 
0.26  313 
0.26  283 
0.26  253 


0.26  223 


0.26  193 
0.26  163 
0.26  133 
0.26  103 
0.26073 
0.26  043 
0.26013 
0.25983 
0-25  953 


0.25  923 


0.25  893 
0.25  863 
0.25  S34 
0.25  804 
0.25  774 
0.25  744 
0.25  714 
0.25  6S4 
"•-'?  655 
0.25  625 


I-  Col  1  c<l   L  Tan 


9-94  451 
9-94  445 
9.94  438 

9-94  431 
9.94  424 
9.94417 
9.94410 
9.94  404 
9-94  397 


■)4  390 


9-94  383 
9-94  376 
9.94  369 

9-94  362 
9-94  355 
9-94  349 
9-94  342 

9-94  335 
9-94  328 


9.94321 


9-94  3M 
9-94  307 
9.94  300 

9-94  293 
9.94  286 
9.94  279 

9-94  273 
9.94  266 

« |.<)4  25.) 


9.94  252 


9-94  245 
9.94  238 
9.94  231 
9-94  224 
9.94  217 
9.94  210 

9-94  203 
9.94  [96 

<>.<)4  189 
944  [82 


1. 


P     P 


31 

30 

I 

05 

0.5 

2 

1.0 

1.0 

3 

1.6 

i-5 

4 

2.1 

2.0 

5 

2.6 

2.5 

6 

3-i 

3.0 

7 

3-6 

3-5 

8 

4-1 

4.0 

9 

4.6 

4-5 

10 

5-2 

5.o 

20 

10.3 

10.0 

30 

15-5 

150 

40 

20.7 

20.0 

50 

25.8 

25.0 

24 

23 

1 

0.4 

0.4 

2 

0.8 

0.8 

3 

1.2 

1.2 

4 

1.6 

1-5 

5 

2.0 

1.9 

6 

2.4 

2-3 

7 

2.8 

2-7 

8 

3-2 

3-i 

9 

3-6 

3-4 

10 

4.0 

3-8 

20 

8.0 

7-7 

30 

12.0 

n.5 

40 

16.0 

15-3 

50 

20.0 

19.2 

29 
0.5 

1.0 

1.4 
1.9 

2-4 

2.9 

3-4 
3-9 
4-4 
4.8 
9-7 
M-5 
19-3 
24.2 

22 

0.4 

0.7 

1.1 

1-5 

1.8 

2.2 

2.6 

29 

3-3 

3-7 

7-3 

11. o 

14.7 

18.3 


I 

7 

O.I 

2 

0.2 

3 

0.4 

4 

0.5 

5 

0.6 

6 

0.7 

7 

0.8 

8 

0.9 

9 

1.0 

10 

1.2 

20 

2-3 

3" 

3-5 

40 

4-7 

50 

5-8 

O.I 

0.2 

0.3 
0.4 

0.5 
0.6 
0.7 
0.8 
0.9 

1.0 

2.0 
3-o 
4.0 
5-o 


' 

(i 

31 

31 

2.2 

2.6 

6.6 

7.8 

1 1.1 

12.9 

15-5 

1S.1 

19.9 

23.2 

24.4 

2S.4 

28.8 

30 

2-5 

7-5 

12.5 

17.5 
22.5 

27-5 


P     P 


331 


r.l 


29 


119°  209°  *299c 


L  Sin 


9-68  557 


9.6S  580 
9.68  603 
9.68  625 
9.68  648 
9.68  671 
9.68  694 
9.68  716 
9.68  739 
9.68  762 


9.68  784 
9.6S  807 
9.68  829 
9.68  852 
9.68  875 
9.68  S97 
9.68  920 
9.68  942 
9.68  965 
9.68  9S7 


9.69  010 


9.69032 
9.69055 
9.69077 
9.69  100 
9.69  122 
9.69  144 
9.69  167 
9.69  1S9 
9.69  212 


9-<>9  234 


9.69  256 
9.69  279 
9.69  301 
9.69  323 
9-6g  345 
9.69  368 
9.69  390 
9.69412 
9-69  434 


9-Q9  45P 
9.69  479 
9.69  501 
9-69  523 

9-69  545 
9.69  567 
9.69  5S9 
9.69  611 
9.69  633 
9-69655 


9-69  677 


9.69  699 
9.69  721 
9-69  743 
9.69  765 
9.69  787 
9.69  809 
9.69  831 

9-6g  853 
9.69  875 


9.69  897 


L  Cos 


L  Tan 


9-74  375 


9-74  405 
9-74  435 
9-74  465 
9.74494 
9-74  5^4 
9-74  554 
9-74  583 
9-74  6I3 
9-74  643 
9-74  673 


cd 


9-74  702 
9-74  732 
9.74  762 

9-74  791 
9.74821 
9-74  85I 
9.74  880 
9.74910 
9-74  939 


9-74  969 

9.74  998 
9-75  028 
9.75058 

9.75  0S7 
9-75  ii7 
9-75  146 
9-75  176 
9-75  205 
9-75  235 


264 


9-75  294 
9-75  323 
9-75  353 
9-75  382 
9-75  4" 
9-75  441 
9-75  470 
9-75  500 
9-75  529 


9-75  558 


9-75  58S 
9.75617 
9-75  647 
9.75676 
9-75  705 
9-75  735 
9.75  764 
9-75  793 
9-75  822 


9-75  8; 


9-75  881 
9.75910 
9-75  939 
9-75  969 
9-75  998 
9.76027 

9.76056, 

9.76086 
9-76ii5 


9.76  144 


L  Cot      c  d 


L  Cot 


0.2:  (".25 
0-25  595 
0.25  565 
0.25  535 
0.25  506 
0.25  476 
0.25  446 
0.25417 
0.25  3S7 
C25  357 


0.25327 


0.25  298 
0.25  268 
0.25  238 
0.25  209 
0.25  179 
0.25  149 
0.25  120 
0.25  090 
0.25  061 


0.25  031 


0.25  002 
0.24  972 
0.24  942 
0.24  913 
0.24  8S3 
0.24  854 
0.24  S24 
0.24  795 
Q-24  765 


0.24  736 


0.24  706 
0.24  677 
0.24  647 
0.24  618 
0.24  589 
0.24  559 
0.24  530 
0.24  500 
0.24471 


0.24442 


0.24412 
0.24  383 
0.24353 
0.24  324 
0.24  295 
0.24  265 
0.24  236 
0.24  207 
0.24  1 7S 


!4M^ 


L  Cos   I  d 


_<».'l4   1>2 


9-94175 
9.94  168 
9.94 161 

9-94154 

9-94  M7 
9.94  140 

9-94  133 
9.94  126 

9-<M  1  [9 


9.' 1 4 


9-94  105 
9-94  098 
9.94  090 
9.94083 
9.94  076 
9.94  069 
9.94  062 
9-94  055 
9-94  04S 


9-94  Q4^ 


9-94  034 
9.94027 
9.94  020 
9.94012 
9.94  005 
9.93  998 
9.93  991 
9-93  984 
9-93  977 


'-'•"-;i-'' 


9-93  963 
9-93  955 
9-93  948 
9-93  941 
9-93  934 
9-93  927 
9.93  920 
9.93912 
9-93  905 


9-93  898 


9.93  891 
9.93  884 
9-93  876 
9.93  869 
9-93  S62 
9-93  855 
9-93  847 
9-93  840 
9-93  833 


9.93  826 


0.24  119 
0.24  090 
0.24061 
0.24031 
0.24  002 
0.23973 
0.23  944 
0.23914 
0.23  885 


0.23  S56 


L  Tan 


9.93  819 
9-93811 
9.93  804 

9-93  797 

9-'»3  7"') 
9.93  782 

9-93  775 
9.93  768 
9-93  760 


9-93  753 


L  Sin   d 


60 


7 

59 

1 
7 

: 
: 
: 
: 
: 
7 

58 

57 

56 

55 

54 

53 

52 
Si 

1 

50 

49 

- 

: 
7 
" 
7 

7 

48 

47 

46 

45 

44 

43 

4? 

i 

41 

/ 

40 

i 

3W 

7 

s 

38 

37 

7 
7 
7 
7 

36 

35 

34 

33 

32 

/ 

V 

; 

30 

8 

2q 

28 

p  p 


30 

29 

I 

0.5 

0.5 

2 

1.0 

1.0 

3 

i-5 

1.4 

4 

2.0 

1.9 

5 

2-5 

2.4 

b 

3.0 

2.9 

7 

3-5 

3-4 

8 

4.0 

3-9 

9 

4-5 

4-4 

10 

5-o 

4.8 

20 

1 0.0 

9.-7 

30 

15-0 

I4S 

4" 

20.0 

19-3 

50 

25.0 

24.2 

22 

8 

1 

0.4 

O.I 

2 

0.7 

0.3 

3 

1.1 

0.4 

4 

i-5 

0.5 

5 

1.8 

0.7 

6 

2.2 

0.8 

7 

2.6 

O.q 

8 

2-9 

I.I 

9 

3-3 

1.2 

m 

3-7 

1-3 

20 

7-3 

2.7 

30 

11.0 

4.0 

40 

14-7 

5-3 

50 

18.3 

6.7 

23 

0.4 
0.8 

1.2 

i-5 

1.9 

2.3 

2.7 

3-1 

3-4 

3-8 

7-7 

u-5 

15-3 

19.2 


0.1 
0.2 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 


2-3 
3-5 
4-7 
5-8 


8 

30 

0 

1.9 

? 

5-6 

3 

9.4 
I3-I 

4 

1 6.q 

5 
6 

7 

8 

20.6 

24-4 

28.1 

7 

30 

0 

2.1 

I 

6.4 

10.7 

3 

15.0 

19-3 

f\ 

23.6 

27.9 

8_ 
29 

1.8 
5-4 
9.1 
12.7 
16.3 
19.9 
23.6 
27.2 


29 

2.1 

6.2 
10.4 
14.5 
1S.6 
22.8 
26.9 


*150°  240°  *330c 


60l 


30c 


120° 


L  Sin 


L  Tan    c  d     L  Cot 


L  ( 'os     cl 


*300° 
P    P 


19 
20 
21 
22 
23 
24 
25 
26 

27 

28 
29 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
4- 
43 
44 
45 
46 

47 
P 
19 
50 

51 
52 
:  i 
54 
55 
56 

57 
58 

BO 


.<".)  -<>; 


69  941 
69963 

69984 
70006 
70028 
70050 

70  093 


•7"  '37 
7oi59 
70'  [80 

70  202 

70  224 
70  245 
70  267 
70288 
70  310 


:• '  3  $2 


70353 
70375 
70396 

70  418 

70439 
70461 

70482 
70504 

70525 


•'>  54: 


70  568 

70590 
70  61 1 

70633 
70654 
70675 
70697 
70718 
70739 


70761 


70782 
70  803 
70  824 
70846 
70867 
70888 
70909 
70931 
70  952 


7"o73 


70  994 

71  015 
71036 
71058 
71079 
71  [00 
71  121 
71    142 

I     ''I 


9-7"  M4 


9-76I73 
9.76  202 
9-76231 
9.76  261 
9.76  290 
9.76319 
9.76348 
9-76  377 
9-76  406 


9-76  435 


9.76464 
9.76493 
9.76522 

9-76  55I 
9.76  580 
9.76  609 
9.76  639 
9.76  668 
0-76697 


9-76  725 


9.76  754 
9.76  783 
9.76  812 
9.76  841 
9.76  870 
9.76  899 
9.76928 
9-76  957 
9.76986 


9-77QI5 


9.77044 
9-77  073 
9.77101 

9-77I30 
9-77  159 

9.77  iSS 

9.77217 
9-77  246 
9-77  274 


9-77  3Q3 


9-77  332 
9-77  36I 
9-77  390 

</-77  4'-s 
9-77  447 
9-77  47'' 
9-77  505 
9-77  533 

9.77  S<»2 


'(•77  59' 


9-77  6I9 

9-77  648 
9-77  677 
9.77  706 

9-77  734 
9-77  763 

9-77  79' 

9.77820 

9  77  *40 


>77  877 


O.23  S56 


9-93  753 


0.23  S27 
0.23  798 
0.23  769 

°-23  739 
0.23  710 
0.23  681 
0.23  652 
0.23  623 
0.23  594 


9-93  746 
9-93  738 
9  93  731 
9-93  724 
9-93  7'7 
9-93  709 
9.93  702 
9-93  695 
9-93  687 


Q-23  565 
0.23  536 
0.23  507 
0.23  478 
0.23  449 
0.23  420 
0.23  391 
0.23  361 
0.23  332 
0.23  303 


9.93  680 


9-93  673 
9-93  665 
9-93  658 
9-93  650 
9-93  643 
9-93  636 
9.93  628 
9.93  621 
9.93614 


0.23  275 


9.93  606 


0.23  246 
0.23217 
0.23  188 
0.23  159 
0.23  130 
0.23  101 
0.23  072 
0.23  043 
0.23  014 


9-93  599 
9-93  591 
9-93  584 
9-93  577 
9-93  569 
9-93  5'62 
9-93  554 
9-93  547 
9.93-539 


0.22  950 
0.22927 
0.22  899 
0.22  870 
0.22  841 
0.22  812 
0.22  783 
0.22  754 
0.22  726 


9-93  52  5 
9-93  517 
9-93  5io 
9-93  502 
9-93  495 
9-93  487 
9.93  480 
9-93  472 
9-93  465 


Q.22  697 


9-93  45  7 


0.22  668 
0.22  639 
0.22  610 
0.22  582 
0.22  553 
0.22  524 
0.22  495 
1  (.22  467 
o.22  438 


9-93  450 
9-93  442 
9-93  435 
9.93427 
9.93  420 
9.93412 

9-93  405 
9-93  397 

.j..)3  30" 


0.22  409 


9.93  >82 


0.22  38I 
O.22352 
0.22  323 
0.22  294 
0.22  266 
0.22  237 
0.22  209 
,,  ^2  1  80 
1.22  1  i 


9-93  375 
9-93  367 

9.93  360 

9.93352 
9.93  [44 
9-93  337 
9.93  329 
9.93  ;jj 
9-93  Ji  l 


30 

29 

28 

I 

0.5 

0.5 

0. 

2 

1.0 

1.0 

o.< 

3 

1-5 

1.4 

4 

2.0 

1.9 

1. 

5 

2.5 

2.4 

2. 

6 

3-o 

2.9 

2. 

/ 

3-5 

3-4 

3- 

8 

4.0 

3-9 

3- 

9 

4-5 

4-4 

4- 

10 

5-o 

4-8 

4- 

20 

10.0 

9-7 

9- 

30 

15-0 

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M- 

40 

20.0 

19-3 

18. 

50 

25.0 

24.2 

23- 

22 

1 

0.4 

2 

0.7 

3 

i.i 

4 

1-5 

5 

1.8 

6 

2.2 

7 

v2.6 

8 

2-9 

9 

3-3 

10 

3-7 

20 

7-3 

30 

11.0 

40 

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5° 

18.3 

8 

1 

0.1 

2 

o-3 

3 

0.4 

4 

0.5 

5 

0.7 

6 

0.8 

7 

0.9 

8 

i.i 

9 

1.2 

id 

i-3 

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2.7 

30 

4.0 

40 

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50 

6.7 

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0.4 
0.7 


2.4 

2.8 
3-2 
3-5 
7.0 
10.5 
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17-5 


0.2 
0.4 

0.5 
0.6 
0.7 
0.8 
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1.0 
1.2 

2-3 

3-5 
4-7 
5-8 


7 

7 

30 

29 

2.1 

2.1 

6.4 

6.2 

10.7 

to.  1 

15-0 

1  1-5 

19-3 

18.6 

23.6 

22.8 

27.9 

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28 
2.0 
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22.0 
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1.93  10 


I.  ( 


L  Cot   !«•  (1     L  Tan 


L 


1 10 


39 


329 


59 


93 


31° 

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3  211°  *301° 

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L  Sin  |  d 

L  Tan 

c  d  L  Cot 

L  Cos  (1 

1'  P 

0 

I 

9.71  184 

-  21 
21 
21 
21 

9-77  S77 

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29 
28 

<»._>_•  123 

9-93  307 

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8 
7 
8 

60 

59 

9.71  205 

9.77  906 

0.22  O94 

9.93  299 

9Q 

28 

2 

9.71  226 

9-77  935 

0.22  O65 

9.93  291 

58 

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2 

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9.71  247 

9-77  963 

29 

0.22  O37 

9.93  284 

57 

0 

3 

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4 
9 

4 

9.71  268 

9.77992 

28 

0.22  OOS 

9.93  276 

7 
g 

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3 

1.4 

1 

5 

9.71  289 

21 

9.7S  020 

29 

28 

0.2I  980 

9.93  269 

55 

4 

1.9 

6 

9.71  310 

21 

9.78049 

0.2I  951 

9.93  26 1 

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9-7i  33i 

9.78077 

29 

29 
28 
29 
28 

0.21  923 

9-93  253 

53 

6 

2.9 

3-4 

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8 

9-71  352 

21 
20 
21 

9.78  106 

0.2I  894 

9.93  246 

8 

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7 

3 

3 

9 
10 

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9-71  373 

9-78  135 

0.2I  865 

9-93  238 

8 
7 
8 
8 

5i 
50 

49 

8 
9 
10 

3-9 

4-4 

4.8 

3 

4 
4 

7 
2 

7 

9-71  393 

9.78  163 

0.2I  837 

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9-7I4I4 

9.78  192 

0.2I  808 

9-93  223 

12 

9-71  435 

21 

9.78  220 

29 

0.2I  780 

9-93  215 

48 

20 

9-7 

3 

13 

9.71  456 

21 

9.78  249 

28 

0.2I  751 

9.93  207 

47 

30 

'4-5 

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0 

14 

9-71477 

9.78277 

29 
28 

0.2I  723 

9.93  200 

8 
8 

46 

40 

19.3 

18 

7 

15 

9.71  498 

21 

9.78306 

0.2I  694 

9-93  192 

45 

50 

24.2 

23 

3 

16 

9-7i  519 

9-78  334 

29 

0.21  666 

9.93  184 

44 

17 

9-71  539 

9-78  363 

28 

0.21  637 

9-93  177 

8 

3 
7 
8 
8 

43 

21 

ZU 

18 

9-71  560 

21 

9.78391 

28 

0.21  609 

9.93  169 

42 

1 

0.4 

0.3 

19 
20 

21 

9.71  581 

21 
20 
21 
21 
21 

9-7S4I9 

29 

28 

29 
28 

0.21  581 

9.93  161 

41 
40 

39 

2 

3 
4 

0.7 
1.0 
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1.8 

0.7 
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9.71  602 

9.78448 

0.21  552 

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9.71  622 

9.78476 

0.21  524 

9.93  146 

22 

9-71  643 

9.78  505 

0.21  495 

9-93  138 

38 

5 
6 
7 
S 

i-7 

23 

24 

9.71  664 

9.71685 

9-78  533 
9.78  562 

29 

28 

0.21  467 
0.21  438 

9-93  131 
9.93  123 

7 
8 
8 

37 
36 

2.4 
2.8 

2.0 

2-3 

2.7 

25 

9.71  705 

21 

21 
20 

9.78  590 

28 

0.21  410 

9-93  "5 

7 

8 

8 

35 

9 
10 
20 

3-2 

3-5 
7.0 

3-o 

3-3 
6.7 

26 

27 

9.71726 
9-71  747 

9.78  618 
9.78  647 

29 
28 

0.21  382 
0.21353 

9-93  108 
9.93  100 

34 
33 

28 

9.71  767 

21 

9.78675 

29  0.21325 

9.93  092 

8 

32 

30 

10.5 

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29 
30 

3i 

9.71  7SS 

21 
20 

9.78  704 

28 
28 
29 

0.21  296 

9.93  084 

8 
8 

3i 
30 
29 

40 
5° 

14.0 
17.$ 

13-3 
16.7 

9.71  809 

9.78  732 

0.21  263 

9-93  077 

9.71  829 

9.78  7O0 

0.21  240 

9.93  069 

32 

9.71  850 

20 

9.78  789 

23 

0.21  211 

9.93061 

s 

2S 

8 

7 

33 

9.71  S70 

21 

9.78  817 

28 

0.21  1  S3 

9-93  053 

27 

1 

O.I 

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34 

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20 

9.78  845 

29 

0.21  155 

9.93  046 

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26 

2 

0.3 

0.2 

35 

9.71  911 

21 

9.78874 

28 

0.21  126 

9-93  038 

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25 

3 

0.4 

0.4 

36 

9.71  932 

20 

9.78  902 

28 

0.21  098 

9.93  030 

8 

24 

4 

0.5 

0.5 

37 

9.71952 

21 

9.78  930 

29 

0.21  070 

9.93022 

23 

5 

0.7 

0.6 

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9-71  973 

21 

9-78  959 

28 

0.21  041 

9.93014 

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22 

6 

0.8 

0.7 

39 
40 
41 

9.71  994 

20 
20 

21 

9.78987 

28 
28 
29 

0.21  013 

9.93  007 

- 

21 
20 
19 

7 
8 

9 

0.9 
1.1 
1.2 

0.8 
0.9 
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9.72014 

9.79015 

0.20  985 

9.92  999 

9-72034 

9-79  043 

0.20957 

9.92991 

42 

9-72055 

20 

9.79072 

28 

0.20  928 

9.92  983 

7 

18 

10 

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1.2 

43 

9.72075 

21 

9.79  100 

28 

0.20  900 

9.92  976 

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20 

2.7 

2-3 

44 

9.72096 

20 
21 

9.79  128 

28 

0.20  872 

9.92  968 

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16 

30 

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3-5 

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9.72  116 

9.79156 

29 

O.20  844 

9.92  960 

15 

40 
50 

5-3 
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4-7 

46 

9-72  137 

20 

9.79185 

28 

0.20  815 

9.92  952 

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14 

47 

9-72  157 
9-72  177 

9.79213 
9.79241 

28 
28 

0.20  787 
0.20  759 

9.92  944 
9.92  936 

13 

43 

20 
21 

B 

12 

49 
50 

5i 

9.72  198 

20 
20 

21 

9.79  269 

28 
29 
28 

0.20  731 

9.92  929 

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B 

10 

9 

8 

8 
30 

8 
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9.72  21S 

9.79297 

(.>.2o  703 

9.92921 

9.72  238 

9.79326 

0.20  674 

9.92913 

0 

52 

9.72259 

20 

9-79  354 

28 

0.20  646 

9.92  905 

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1.1 

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13.1 
16.5 

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53 
54 

9.72279 
9.72  299 

20 
21 

9-79  382 
9.79410 

28 
28 

0.20  6l8 
0.20  59O 

9.92  S97 
9.92  889 

3 
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8.8 
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9.72  320 

20 

9-79  438 

28 

0.20  562 

9.92881 

7 
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5 

4 

15. 8 

56 

9.72340 

20 

9.79466 

29 

0.20  534 

9.92  874 

4 

5 
6 

19.2 

57 

9.72  360 

21 

9-79  495 

28 

0.20  505 

9.92  866 

- 

3 

24.4 

23. ( 

22.8 

5S 

9.72381 

20 

9-79  523 

28  0.20477 

9.92  858   g 

2 

I 

28.1 

27.: 

26.2 

59 

9.72  401 

20 

9-79  55i 

28 

0.20  449 

9.92  850  j 

s 

I  1    u 

60 

9.72421 

9-79  579 

0.20421 

1.92  S42 

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L  Cos  1  d   L  Cot  j  c  cl  1  L  Tan 

L  Sin  |  d  1           P  P 

*148°     238°     S32S; 


58c 


94 


32< 


*122°    212c 


^nii': 


L  Sin 


I  tl 


L  Tan     e  d     L  Cot 


L  Cos 


■»•:-'  4-1 


9-79  57" 


9-72  441 
9.72461 
9.72482 

9.72  502 
9.72  522 

9-72  542 
9-72  562 
9.72  582 
9.72  602 


9.72  622 


9.72  643 
9.72  663 
1,7ft  683 

9.72  703 

9-72  723 
9-72  743 
9.72  763 
9.72  783 
9.72  803 


9.72  823 


9-72  843 
9.72  863 
9.72  883 
9.72  902 
9.72  922 
9.72  942 
9.72  962 

9.72  982 

9.73  002 


9-73  Q2i 


9.73041 
9.73  061 
9.73  081 
9.73  101 
9-73  121 
9.73  140 
9.73  160 
9.73  [80 

1.7  1  2(».) 


9-73  219 


9-73  239 
9-73  259 
9-73  278 
9.73  298 
9-73  318 
9-73  337 
9-73  357 
9-73  377 
9-73  396 


9-73  416 
9-73  135 
9-73  455 
9-73  474 
9-73  494 
9-73  513 
9-73  533 
9-73  552 
9-73  572 
9-73  591 


'>-73  6n 

I.   (OS 


9.79  607 
9-79  635 

9.79  663 

9.79  69I 
9.79719 

9-79  747 
9-79  776 
9.79804 
9-79832 


9.79  860 
9.79888 
9.79916 
9-79  944 
9.79972 

9.80  000 
9.80028 
9.S0056 
9.80084 
9.80  112 


9.80  140 


9  80  168 
9.80195 
9.80223 
9.80  251 
9.80  279 
9.S0307 

9-80  335 
9.80  363 
9-80  39I 


9-b°4i9 


9.60447 
9.80  474 
9.80  502 
9.80  530 
9.80558 
9.80586 
9.80614 
9.80  642 
9.80  669 
9.80  697 


9-8o  725 
9-8o  753 
9.80  781 
9.80  808 
9.80836 
.,.-0  ;m,4 
9.80  892 
9.80  919 
9-8o  947 


-).*<>  975 


9.81  003 
9.81  030 
9.S1  058 
9.81  086 
9-8i  113 
9.81  141 
9.81  169 
9.81  196 
9-8t  224 


9.81  252 


0.20  393 
0.20  365 
0.20337 

9.92  834 
9.92  826 
9.92  818 

O  CO    in 
CO  CM    CI 

CI    CI    CI 

odd 

9.92  810 
9.92  803 
9-92  795 

0.20  224 
0.20  196 
0.20  168 

9.92  787 
9.92  779 
9.92  77! 

0.20  140 


9.92  763 


0.20  112 
0.20  084 
O.2OO56 
0.20  028 
0.20  OOO 

O.I9972 
O.I9944 
O.I9  916 
0.19888 


9-92  755 
9.92  747 
9.92  739 
9.92  731 
9.92  723 
9.92715 
9.92  707 
9.92  699 
9.92  691 


0.19  860 


9-92  683 


0.19832 
0.19  805 
0.19  777 
0.19749 
0.19  721 
0.19693 
0.19  665 
0.19637 
0.19  609 


9.92675 
9.92  667 
9.92  659 
9.92  651 
9.92  643 
9-92  635 
9.92  627 
9.92  619 
9.92  611 


0.19  581 


■>-'i2  t«>\ 


O.I9  553 
0.19  526 
0.19498 
0.19  470 
0.19442 
0.19  414 
0.19  386 
0.19358 
Q-I9  33I 


9-92  595 
9.92  587 
9-92  579 
9-92  57i 
9-92  563 
9-92  555 
9.92  546 
9-92  538 
9-92  53o 


".  ii)  303 


9-92  522 


0.19275 
0.19247 
0.19  219 
0.19  192 
0.19  164 
0.19  136 
0.19  108 
0.19  081 
0-I9  053 

(l.K)  (12? 


9.92  514 
9.92  506 
9.92  498 
9.92  49O 
9.92  482 

9-92  473 
9.92  465 
9-92  457 
9.92  449 


9-<)2   \\\ 


0.1s  997 
0.18  970 
0.18  942 
0.18  914 
0.18  887 
0.18  859 
0.18  831 
0.18  804 
0.18  776 


9-92  433 
((.0242  = 
9.92416 
9.92  408 
9.92  40c 
9.92  392 
9.92384 
9.92  37'' 

i).o2  3": 


0.18  748 


9.92  359 


29 

28 

I 

0.5 

0.5 

2 

1.0 

0.9 

3 

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i-4 

4 

1.9 

1.9 

5 

2.4 

2-3 

6 

2.9 

2.8 

7 

3-4 

3-3 

8 

3-9 

3-7 

9 

4-4 

4.2 

10 

4-« 

4-7 

20 

9-7 

9-3 

30 

14-5 

14.0 

40 

19-3 

18.7 

50 

24.2 

23-3 

21 

20 

1 

0.4 

0.3 

2 

0.7 

0.7 

3 

1.0 

1.0 

4 

1.4 

i-3 

5 

1.8 

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6 

2.1 

2.0 

7 

2.4 

2-3 

8 

2.8 

2-7 

9 

3-2 

3-0 

10 

3-5 

3-3 

20 

7.0 

6.7 

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10.5 

1 0.0 

40 

14.0 

13.3 

50 

17-5 

16.7 

9 

8 

1 

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2 

0.3 

0.3 

3 

0.4 

0.4 

4 

0.6 

0.5 

5 

0.8 

0.7 

6 

0.9 

0.8 

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0.9 

8 

1.2 

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9 

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1.2 

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20 

3-0 

2-7 

30 

4-5 

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50 

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29 

28 

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9.1 

8.8 

12.7 

12.2 

16.3 

15.8 

19.9 

19.2 

23.6 

22.8 

27.2 

26.2 

L  Col     ctl     L  Ta 


2:jt°    »327e 


95 


38° 

123° 

213 

D  *303° 

L  Sin 

a 

L  Tan 

cd 

L  Col 

L  Cos 

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9-73  6n 

19 

9.81  252 

27 
28 

2S 

0.18  74S 

9-92  359 

s 

60 

59 

9-73  630 

9.81  279 

0.18  721 

9.92351 

28 

27 

2 

9-73  650 

20 

9-Si  307 

0.18  693 

9-92  343 

- 

58 

1 

0-5 

0.4 

3 

9.73  669 

19 

9-8i  335 

0.18665 

9-92  33! 

- 

57 

2 

0.9 

0.9 

4 

9.73  689 

20 

9.81  362 

27 

28 

0.18638 

9.92  326 

9 

56 

3 

1-4 

1.4 

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5 

9.73  708 

19 

9-Si  390 

0.18  610 

9.92  318 

- 

55 

4 

1.9 

6 

9-73  727 

19 

20 

9.81  418 
9.81  445 

28 
27 

0.18  582 

0.18555 

9.92  310 

■s 
S 

54 

5 
6 

2-3 
2.8 

2.2 

2-7 

7 

9-73  747 

28 

9.92  302 

53 

7 
8 

3-3 
3-7 
4.2 
4-7 
9-3 

3-2 

3.6 

4.0 

4-5 
9.0 

8 

9-73  766 

l9 

9.81473 

0.18  527 

9.92  293 

9 

S2 

9 
10 

9-73  735 

19 
20 

9.81  500 

27 
28 
28 

M.I  >  ^1  II  1 

9-92  285 

8 
8 

51 
50 
49 

9 
10 
20 

9-73  805 

9.81  528 

0.1S  472 

9.92  277 

9.73  S24 

9-8i  556 

0.18444 

1  |.i)2  21") 

12 

9-73  343 

19 

9-Si  583 

27 
28 

0.18  417 

9.92  26o 

9 

43 

30 

14.0 

•3-5 

13 

9-73  863 

20 

9.81  611 

0.18  3S9 

9.92  252 

8 
8 

47 

40 

18.7 

18.0 

14 

9.73  SS2 

x9 

9.81  638 

27 

28 

0.18362 

9.92  244 

46 

50 

23-3 

22.5 

15 

9.73  901 

x9 

9.81  666 

0.18  334 

9-92  235 

9 

8 
8 
8 

45 

16 

9.73921 

20 
19 

9.81  693 

27 

28 

0.1S  307 

9.92  227 

44 

20 

19 

18 

17 

9-73  940 

9.81  721 

0.18  279 

9.92  219 

43 

1 

0.3 

0.3 

0.3 

18 

9-73  959 

19 

9.81  748 

27 

28 
27 
28 

0.18  252 

9.92  211 

42 

2 

0.7 

0.6 

0.6 

19 
20 

21 

9-73  978 

19 
19 
20 

9.81  776 

0.18  224 

9.92  202 

9 

8 
8 

4i 
40 

39 

3 
4 

5 

1.0 

i-3 
i-7 

1.0 
i-3 
1.6 

1.2 

i-5 

9-73  997 
9.74017 

9.S1  S03 

0.18  197 

9.92  I94 

9.81  S31 

0.18  169 

9.92  186 

22 

9.74036 

19 

9.81  858 

27 

28 

0.18  142 

9.92  177 

9 

38 

6 

2.0 

1.9 

1.8 

23 

9-74  055 

19 

9.81  886 

0.18  114 

9.92  169 

8 

37 

7 

2-3 

2.2 

2.1 

24 

9.74074 

19 

9-81  913 

27 

28 

0.18087 

9.92  l6l 

8 

36 

8 

9 
10 
20 

2-7 
3-o 
3-3 
6-7 

2-5 
2.8 

2.4 
2-7 

25 

9-74  093 

19 

9.81  941 

0.18059 

9.92  152 

9 

35 

3-2 

6.3 

26 

9-74  "3 

20 
l9 

9.81  968 

27 
28 

0.18032 

9.92  I44 

8 
8 

34 

3-o 
6.0 

27 

9-74  132 

9.81  996 

0.18  004 

9.92  I36 

33 

30 

10.0 

9-5 

9.0 

28 
29 

30 
31 

9-74  151 
9-74  170 

x9 
19 
19 
19 

9.82  023 
9.S2  051 

27 

28 
27 
28 

0.17977 
0.17949 

9.92  127 
9.92  Ilg 

9 

8 

S 

9 

32 
3i 
30 

29 

40 
50 

13-3 
16.7 

12.7 
K.8 

12.0 
1^.0 

9.74  1S9 

9.S2  07s 

0.17  922 

9.92  III 

9.74  208 

9.82  106 

0.17894 

9.92  I02 

Q 

8 

O.I 

0.3 
0.4 

32 

9.74227 

19 

9.82  133 

27 
2S 
27 

0.17  867 

9.92  O94 

S 
8 
9 
8 

28 

0.2 
0.3 

0.4 

33 
34 

9.74246 
9.74265 

19 
19 

9.82  161 
9.82  188 

0.17839 
0.17  812 

9.92086 
9.92077 

27 
26 

2 

3 

35 

9.74  2S4 

l9 

9.82  215 

27 
28 
27 
28 

0.17785 

9.92  069 

25 

4 

0.6 

0.5 

36 

9-74  303 

19 
19 

9.82  243 

O.I7  757 

9.92  060 

9 

8 

8 

24 

5 

0.8 

0.7 

37 

9.74322 

9.82  270 

0.17730 

9.92  052 

23 

6 

0.9 

0.8 

33 

9-74  341 

J9 

9.82  298 

0.17  702 

9.92  044 

22 

7 

1.0 

0.9 

39 
40 
4i 
42 

9.74360 

19 

19 
19 
19 

9.82  325 

27 

27 
28 

27 

28 
27 

0.17675 

9.92035 

9 

s 

9 

8 
8 
9 
8 
9 

21 
20 

19 

18 

8 

9 
10 
20 

1.2 
14 
i-5 
3-0 

1.1 
1.2 
i-3 

9-74  379 

9.82352 

0.17648 

9.92027 

9-74  39S 
<J-74  4i7 

9.82  3S0 
9.82  407 

0.17  620 
O.I7  593 

9.92  Ol8 
9.92  OIO 

43 
44 

9-74  436 
9-74  455 

19 

19 

9-82  435 
9.82  462 

0.17565 
0.17  533 

9.92  002 

9-91  993 

17 
16 

3° 
40 
5° 

4-5 
6.0 

7.5 

4.0 
5-3 
6.7 

45 
46 

9-74  474 

l9 
19 
19 

9.82489 
9-82517 

27 

28 

0.17  511 
0.17483 

9.91  985 
9.91  976 

1 5 

9-74  493 

27 

M 

47 

9-74  512 

9.82  544 

0.17456 

9.91  968 

13 

()    (1    0 

43 

9-74  531 

l9 

18 

19 
19 

9.82571 

27 
28 
27 
27 
2& 

0.17429 

9-91  959 

9 

8 

9 
8 

12 

0 

49 
50 
5i 

9-74  549 

9.82  599 

0.17  401 

9.91  951 

11 
10 
9 

28 

07 

27 

i-7 

9.74  568 

9.82  626 

o.i7  374 

9.91  942 

0 

[.6 

4-7 

7.8 

10.9 

9-74  587 

9-82653 

O.I7  347 

9-91  934 

4 

.J 

52 

9.74  606 

l9 

9.82  681 

0.17  319 

9.91  925 

9 

8 

9 

8 

8 

2 

■s 

•  5 

11.8 

53 

9-74625 

19 
19 

18 

9.82  708 

27 

0.17  292 

9.91  917 

7 

3 

10 

54 

9-74  644 

9-82  735 

'' 

0.17265 

9.91  90S 

6 

4 

14.0 

13 

•5 

15-2 

55 

9.74  662 

9.82  762 

27 

2S 

0.17238 

9.91  900 

5 

5 
6 

17.1 

n 

•5 

18.6 

56 

9.74  6S 1 

J9 

9.82  790 

0.17  210 

9.91  891 

9 
8 

4 

20.2 

19 

■S 

21.9 

'  57 

9-74  700 

x9 

9.82  817 

27 

0.17  183 

9.91  883 

3 

8 

23-3 

22 

•5 

25-3 

53 

9-74  719 

19 

18 

19 

9.82  844 

27 

0.17  156 

9.91  874 

9 

8 

9 

2 

9 

26.4 

25-5 

— 

59 
60 

9-74  737 

9.82  871 

27 
28 

0.17  129 

9.91  866 

0 

9-74  756 

Q.S2  899 

0.17  IOI 

i).(ii  --- 

L  Cos 

d 

L  Cot 

cd 

L  Tan 

L  Sin 

(1 

P  P 

T46°     236° 


::2i; 


5GC 


96 


Lsii 


3£ 

L  Tan     c  d  I    L  Cot      L  Cos   I  d 


124  = 


f304< 


9-7-1 


'1.74  77? 
(.74  794 
9-74  S12 
9.74831 
9.74  850 
9.74  868 

9.74887 

9.74906 

O.74  .)24 


9.82  S99 


9-74  943 


9.74961 
9.74980 
9.74999 
9-75  0I7 
9-75  036 
9-75  054 
9-75  073 
9-75  09I 
9-75  no 


9.75  128 


9-75  M7 
9-75  165 
9-75  184 
9.75  202 
9-75  221 
9-75  239 
9-75  25^ 
9-75  276 
9-75  294 


9-75  313 


9-75  331 
9-75  350 
9.75  368 
9-75  386 
9-75  405 
9-75  423 
9-75  441 
9-75  459 
9-75  478 


9-75  496 


9-75  5M 
9-75  533 
9-75  55i 

<;-75  5^7 
9-75  605 
9.75  624 
9.75642 
9.75  660 


9.75678 


9-75  696 
9-75  714 
9-75  733 
9-75  75i 
9-75  7'»» 
9-75  787 
9-75  805 
9.75  823 
9-75  84] 
■>-7;  ■--'» 

L  Cos 

1  IS 


9.82  926 
9.82953 
9.S2  980 

9.83  008 
9-83  035 
9.83  062 

9.83  089 
9.83117 

9.83  '44 


9-83  HI 


9.83  198 
9.83  225 
9.83  252 
9.83  280 
9-83  307 
9-83  334 
9-83  36I 
9-83  388 
9.83415 


9-83  442 


9.83  470 
9-83  497 
9-83  524 
9-83  55I 

9-83  578 
9. S3  605 

9.83  632 

9-83  659 
9.83686 


9-a3  713 


9-83  740 
9.83  768 
9-83  795 
9.83  822 
9.83  849 
9.83  876 
9.83  903 
9-83  930 
9-83  957 


9-83  984 
9.84  01 1 
9.S4038 
9.84065 
9.84092 
9.84119 
9.84  146 
9.84  173 
9.84  200 
9.K4227 


9-84  254 


9.84  2S0 
9.84  307 
9-84  334 
9.84  361 

9-84  388 

.,..-  )  (1  = 
9.84    II-' 

9.8  1  r  9 
9.84  i'-' 


,.- 1  523 


[Ol 


9.91  857 


0.17074 
0.17047 
0.17020 
0.16  992 
0.16965 
0.16938 
0.16  911 
0.16883 
0.16856 


9.91  849 
9.91  840 
9-9i  832 
9.91  823 
9-91  815 
9.91  806 
9.91  798 
9.91  789 
9.91  781 


0.16  829 


9-91  772 


I. 


.t   <•(! 


0.16  802 
0.16775 
0.16  74S 
0.16  720 
0.16  693 
0.16666 
0.16639 
0.16  612 
0.16  585 


9.91  763 

9-9i  755 
9.91  746 

9.91  738 
9.91  729 
9.91  720 
9.91  712 
9.91  703 
9.91  695 


0.16  558 


9.91  686 


0.16  530 
0.16  503 
0.16476 
0.16449 
0.16  422 
0.16  395 
0.16368 
0.16  341 
o.i6  314 


9.91  677 
9.91  669 
9.91  660 

9-91  651 
9.91  643 
9.91  634 
9.91  625 
9.91  617 
9.91  608 


0.16  287 


9-91  599 


0.16  260 
0.16  232 
0.16  205 
0.16  178 
0.16  151 
0.16  124 
0.16097 
0.16070 

11.  Id  1  143 


9.9I  59I 
9-91  582 

9-9i  573 
9-9i  565 
9-9i  556 
9-91  547 
9-91  538 
9-91  530 
9.91  521 


0.16  016 


9-9r5i 


0.15989 
0.15  962 

O.I5  935 
0.15  908 
0.15  881 
0.15854 
0.15827 
0.15  800 
O.I5  773 


9.91  504 

9-91  495 
9.91  486 

9.91  477 
9.91  469 
9.91  460 
9.91  451 
9.91  442 
9.91  1  1  l 


0.15  74'' 


0.15  720 
0.15693 
0.15  666 
0.15  639 
0.15  612 
0.15585 
O.I5  558 
0.15  531 
"•15  5»4 


"■'5  477 

L  Tan 


9.91  425 
9.91  416 
9.91  407 
9.91  398 

189 

.,.,,.  381 
9.91  372 
9.91  363 
9.9]  154 
9-91  345 
')■')'  33'' 
1.  Sin 


28 

27 

2fi 

0.5 

0.4 

0.4 

0.9 

0.9 

0.9 

1.4 

1.4 

i-3 

1.9 

1.8 

i-7 

2.3 

2.2 

2.2 

2.8 

2-7 

2.6 

3-3 

3-2 

3.0 

3-7 

3-6 

3-5 

4-2 

4.0 

3-9 

4-7 

4-5 

4-3 

9-3 

9.0 

8.7 

14.0 

13-5 

13.0 

18.7 

18.0 

17-3 

23-3 

22.5 

21.7 

19 

1 

0.3 

2 

0.6 

3 

1.0 

4 

i-3 

5 

1.6 

6 

1.9 

7 

2.2 

8 

2.5 

9 

2.8 

10 

3-2 

20 

6-3 

30 

9-5 

40 

12.7 

50 

15-8 

9 

1 

0.2 

2 

0.3 

3 

0.4 

4 

0.6 

5 

0.8 

6 

0.9 

7 

1.0 

8 

1.2 

9 

1.4 

10 

i-5 

20 

•  3-0 

30 

4-5 

40 

6.0 

5° 

7.= 

18 

0.3 
0.6 
0.9 
1.2 
i-5 
1.8 


2.4 
2.7 
3-o 
6.0 
9.0 
12.0 
15.0 


0.1 
0.3 
0.4 
0.5 
0.7 
0.8 
0.9 
1.1 
1.2 
i-3 
2-7 
4.0 

5-3 

6.7 


9 

8 

lis 

28 

1.6 

1.8 

? 

4-7 

5-2 

3 

7.8 

8.8 

4 
5 
6 

to.g 

12.2 

1  y.o 

C5-8 

'7  1 

M.J 

20.2 

/ 
9 

23-3 

26.4 



i-7 
5-i 
8.4 
[i.8 

15-2 

1  8.6 
25.3 


I'     P 


::-j: 


97 


L  Sin 


L  Tan   |  cd 


35° 

L  Cot 


LCos      (l 


*305° 
P    P 


9-75  859 


9-75  »77 
9-75  895 
9-75  9*3 
9-75  931 
9-75  949 
9-75  967 

9-75  985 
9.76003 
9.76021 


9.70  039 


9.76057 
9.76075 
9.76093 
9.76  in 
9.76  129 
9.76  146 
9.76  164 
9.76  162 
9.76  200 


9.76216 


9.76236 
9-76253 
9.76271 
9.76  289 
9.76307 
9.76324 
9.76  342 
9.76360 
9-76370 


9-76  395 


9-76  413 
9.76431 
9.76  44S 
9.76466 
9.76484 
9-76  501 
9.76519 
9-76  537 
9-76  554 


9-76  572 


9.76  590 
9.76  607 
9.76625 
9.76642 
9.76  660 
9.76677 
9.76695 
9.76712 
9-76  730 


9-76  747 


9.76  765 
9.76782 
9.76  800 
9.76817 
9.76835 
9-76  852 
9.76  870 
9.76887 
9-76904 


9.7692 


L  Cos 


9-84523 


9-84  550 
9.84  576 
9.84  603 
9.84  630 
9.S4657 
9.84684 

9-84  7" 

9.84  73S 
9.84  764 


9-84  79' 


9.84  S18 
9.84  845 
9.S4  872 

9.84  S99 
9.84925 
9.S4952 
9.84979 

9.85  006 
9.S5033 


9-85Q59 


9.85086 
9-85II3 
9-85  MO 
9.85  166 
9-S5  193 
9.85  220 

9-85  247 
9-85  273 
9.85  300 


9-85  327 


9-85  354 
9.85  380 
9.85  407 

9-85  434 
9.85  460 
9.85487 

9-85  5I4 
9.S5  540 
9-85  567 


9-85  594 


9.85  620 
9.85  647 
9.85  674 
9.85  700 
9.85  727 
9-85  754 
9.85  780 
9.85  807 
9-85  834 


9.85  860 


9.85  887 
9.85913 
9.85  940 
9.85  967 
9-85  993 
9.86020 

9.S6046 
9.S6073 
9.S6  100 


9.86  126 


L  Cot     cd 


0-15  4: 


9.91 


0.15450 
0.15424 
0.15397 
0.15370 
0.15343 
0.15  316 

0.15  289 
0.15  262 
0.15  236 


336 
9-91  328 
9.91  319 
9.9 1  310 
9.91  301 
9.91  292 
9.91  283 
9.91  274 
9.91  266 
9.91  257 


0.15  209 


9-91  248 


0.15 182 
0.15  i55 
0.15  128 

0.15  101 
0.15075 
0.15  04S 
0.15  021 
O.I4  994 
0.14967 


O.M94I 


9.91  239 
9.91  230 
9.91  221 
9.91  212 
9.91  203 
9.91  194 

9-91  185 
9.91  176 
9-9i  167 


0.14914 
0.14887 
0.14  860 
0.14  S34 
0.14  807 
0.14  780 

O.I4  753 
0.14727 
0.14  700 


9.91 


158 


9.91  149 
9.91  141 
9-91  132 
9.91  123 
9.91  114 
9-91  105 
9.91  096 
9.91  0S7 
9.91  07S 


0.14673 


0.14  646 
0.14  620 
O.I4  593 
0.14  566 
0.14  54o 
0.14  5i3 
0.14486 
0.14  460 
O.I4  433 


9.91  069 


0.14406 


9.91  060 
9.91  051 
9.91  042 

9-91  °33 
9.91  023 
9.91  014 
9.91  005 
9.90  996 
9-90987 


9.90  978 


0.14  380 
O.I4  353 
0.14  326 

0.14  300 
0.14273 
0.14  246 
0.14220 
0.14  193 
0.14  166 


0.14  140 


0.14  113 
0.14087 
0.14060 
0.14033 
0.14007 
0.13  980 
O.I3  954 
0.13927 
0.13  900 


0.13874 


L  Tan 


9.90  969 
9.90  960 
9.90951 
9.90  942 

9-9°  933 
9.90  924 

9.90915 
9.90  906 
9.90  896 


9.90  887 


9.90878 
9.90  869 
9.90  860 
9.90851 
9.90  842 
9.90  832 
9.90823 
9.90814 
9.90  805 


9.90  796 


27 

26 

I 

0.4 

0.4 

2 

0.9 

0.9 

3 

i-4 

i-3 

4 

1.8 

1-7 

5 

2.2 

2.2 

6 

2-7 

2.6 

7 

3-2 

3-o 

8 

3-6 

3-5 

9 

4.0 

3-9 

10 

4-5 

4-3 

20 

9.0 

8.7 

30 

13-5 

13-0 

40 

18.0 

17-3 

50 

22.5 

21.7 

0.3 
0.6 

0.9 

1.2 

i-5 
1.8 

2.1 
2.4 
2.7 
3-o 
6.0 
9.0 
12.0 
15.0 


17 

10 

9 

I 

0.3 

0.2 

0.2 

2 

0.6 

0-3 

0.3 

3 

0.8 

0.5 

0.4 

4 

1.1 

0.6 

5 

i-4 

0.8 

0.8 

6 

1-7 

1.0 

0.9 

7 

2.0 

1.2 

1.0 

8 

2-3 

1-3 

1.2 

9 

2.6 

i-5 

1.4 

10 

2.8 

i-7 

i-5 

20 

5-7 

3-3 

3-o 

30 

*.f 

5-o 

4-5 

40 

ii-3 

6-7 

6.0 

50 

14.2 

8-3 

7-5 

10 

27 

i-4 

2 

4-i 
6.8 

3 
4 

9-4 

12.2 

5 
6 

7 

8 

14.8 
17.6 
20.2 

22.9 

9 

25.6 

10 

•J  7 


3-9 
6.5 
9.1 
11. 7 
Mo 
16.9 
19.5 
22.1 
24.7 


26 


1.5 

1.4 

4-5 

4-3 

7-5 

7-2 

10.5 

IO.I 

13-5 

13.0 

16.5 

15-9 

19.5 

18.8 

22.5 

21.7 

25-5 

24.6 

8 

0.1 
0.3 
0.4 
0.5 
0.7 
0.8 
0.9 


i-3 
2-7 
4.0 
5.3 
6.7 


-144       234c 


^24c 


.)! 


98 


30° 


*126°     216°     *306° 


L  Sin 


L  Tan  j  c  d  [ 


L  Cot 


L  Cos 


p  r 


9.76922 


.SO  126 


9.76939 
9.76957 

9.76  991 
9.77009 

9.77  026 

9-77  043 
9.77  061 

9.77078 


095 


9.77  112 
9-77  130 
9-77  M7 
9.77  164 
9-77i8i 
9.77199 
9.77  216 
9-77  233 
9-77  250 


9-77  268 


9-77  285 
9.77  302 
9-77  319 

9-77  336 
9-77  353 
9-77  370 
9-77  387 
9-77  405 
9-77  422 


77  43V 


9-77  456 
9-77  473 
9-77  49° 
9-77  507 

9-77  524 
9-77  541 
9-77  558 
9-77  575 
9-77  592 


9-77  609 


9.77  626 
9-77  643 
9.77  660 

9-77  677 

9.77  694 

9-77  7" 
9.77  728 

9-77  744 
'J.77761 
9-77  778 


9-77  795 
9-77  3i2 

9.77  829 

9-77  846 
9-77  862 

9.77879 
9-77  B96 

9-77  9>  3 
9-77  93" 


77  946 


9-86  153 
9.86  179 
9.86  206 
9.S6  232 
9.86  259 
9.86285 
9.86312 
9-86338 
9-86365 
9.86  392 


9.86418 
9.86445 
9.86471 
9.86498 
9.86  524 
9-86551 
9.86577 
9.86  603 
9.86  630 


9. 86  656 


9.86  683 
9.86  709 
9-86  736 
9.86  762 
9.86  789 
9.86815 
9.86  842 
9.86  868 
9.86  894 


9.86  921 


9.86947 
9-86  974 
9.87  000 
9.87027 
9-87053 
9.87079 

9.87  106 
9-87132 

9-87158 


I.  c< 


9-87185 

9.87  211 
9.87238 
9.S7  264 
9.87  29O 
9-87  3I7 
9-87  343 
9.87369 
9.S7  396 
9-87  422 

<^7-H- 
9-87  475 
9-87  501 
9.87527 

9-87  554 
9.87  580 
9.87  606 

9-87633 
9.87659 
9.87  685 

9-s7  7" 


27 
26 
27 
26 

27 
26 
27 

26 

27 

I     27 

26 

27 
26 
27. 
26 

27 
26 


L  Cot      cd 


_u-:3S74_ 

0.13  847 
0.13  821 
0.13  794 
0.13  768 
0.13  741 
O.I3  715 
0.13  6S8 
0.13  662 
0.13635 


9.90  796 


9.90  787 
9.90  777 
9.90  768 

9-9°  759 
9.90  750 
9.90  741 
9.90  731 
9.90  722 
9-90  7I3 


0.13  608 


9.90  704 


0.13  582 
O.I3  555 
0.13  529 

0.13  502 
0.13476 
O.I3  449 
0.13423 
O.I3  397 
0.13  370 


9.90  694 
9.90  6S5 
9.90  676 
9.90  667 
9.90657 
9.90  648 
9.90  639 
9.90  630 
9.90  620 


o- 1 3  344 
0.13317 
0.13  291 
0.13  264 
0.13  238 
0.13  211 
0.13  185 
0.13  158 
0.13  132 
0.13  106 


9.90  611 


0-13079 


0.13  053 
0.13  026 
0.13  000 
0.12  973 
0.12947 
0.12  921 
0.12  894 
0.12  S68 
0.12  842 


0.12  815 


0.12  789 
0.12  762 
0.12  736 
0.12  710 
0.12  683 
0.12657 
0.12  631 
o.  1 2  604 
0-12578 

O.I2  552 
O.I2  525" 
O.I2499 
O.12473 
O.I2446 
O.I2420 
0.12  394 
O.I2  367 
O.I2  341 
"■12  315 


O.I2  289 


L  Tan 


9.90  602 
9.90  592 
9-90  583 
9-90  574 
9-9°  565 
9-90  555 
9.90  546 
9-90  537 
9-9Q  527 


9.90  518 


9.90  509 
9.90  499 
9.90  490 
9.90480 
9.90471 
9.90  462 
9.90452 
9-90  443 
9-9Q  434 


9.90  424 


9.90415 
9.90  405 
9.90  396 
9.90  386 
9-90  377 
9.90  368 

9.90  358 
9.90  349 
9.90  339 
9.90330 


9.90  320 
9.90  311 
9.90  301 
9.9O  292 
9.90282 
9.90273 
9.91 1263 
9.90254 
'>.•)<>  -'I  I 


')-■>"  23? 


L  Sin 


27 

I 

0.4 

2 

0.9 

3 

1.4 

4 

1.8 

S 

2.2 

6 

2-7 

7 

3-2 

8 

3-6 

9 

4.0 

10 

4-5 

20 

9.0 

30 

13-5 

40 

18.0 

50 

22.5 

26 

0.4 

0.9 

i-3 

1-7 

2.2 

2.6 

3-o 

3-5 

3-9 

4-3 

8.7 

13-0 

17-3 

21.7 


18 

17 

I 

0.3 

0.3 

2 

0.6 

0.6 

3 

0.9 

0.8 

4 

1.2 

I.I 

5 

i-5 

1.4 

6 

1.8 

i-7 

7 

2.1 

2.0 

8 

2-4 

2-3 

9 

2-7 

2.6 

10 

3.0 

2.8 

20 

6.0 

5-7 

30 

9.0 

8-5 

40 

12.0 

"•3 

50 

15-0 

14.2 

16 

0.3 
0.5 
0.8 


i-3 
1.6 
1.9 

2.1 

2.4 

2-7 
5-3 


10 

I 

0.2 

2 

0.3 

3 

0.5 

4 

0.7 

5 

0.8 

6 

1.0 

7 

1.2 

8 

i-3 

9 

i-5 

10 

i-7 

20 

3-3 

30 

5-o 

40 

6.7 

50 

8-3 

0.2 

0.3 
0.4 
0.6 
0.8 
0.9 

1.0 

1.2 

i-4 
i-5 
3-o 
4-5 
6.0 
7-5 


9 

27 

0 

1-5 

?. 

4-5 

3 
4 
5 
6 

7-5 

10.5 
13-5 

16.5 

19-5 

s 

22.5 

'1 

25-5 

so 

1.4 

4-3 

7-2 

10.1 

13.0 

15-9 
18.8 
21.7 
24.6 


1'  I' 


li;; 


37° 

L  Sin      d      L  Tan     c  d     L  Cot       L  Cos 


99 


9.77946 


9-77  9^3 
9.77980 
9-77  997 
9.78013 
9.78  030 
9.78  047 
9.78  063 
9.78  080 
9.78097 


9-78  "3 


9-78  130 
9.78  147 
9.78  163 
9.78  1S0 
9.78  197 
9.78213 
9-78  230 
9.78  246 
9-78263 


9.78  280 


9.78  296 
9-78  3I3 
9.78  329 

9.78  346 
9.78  362 
9-78  379 
9-78  395 
9.78412 
9.78428 
9-75  445 


9.76401 
9.78478 

9.7S  494 

9-78510 

9-78  527 
9-78  543 
9.78  560 
9.78  576 
9-78  592 


9.78  609 


9-78625 
9.78  642 
9.78658 
9.78  674 
9.78  691 
9.78  707 
9.78  723 
9-78  739 
9.7S  756 


9-78  772 


9.78  788 
9.78  805 
9.78  821 
9.78  837 
9.78853 
9.78  869 
9.78  886 
9.78  go2 
9-78918 


9-78  934 


9.8771 


2.-M 


9.87  738 
9.87  764 
9.87  790 
9.87817 
9.87  843 

9.S7  869 

9.87895 

9.87  922 
9-S7  948 


9.87974 


9.88  000 
9.88027 
9.88053 
9.88  079 
9.88  105 
9.88  131 
9.8S  158 
9.88  184 
9.88  210 


9.88  236 


9  88  262 
9.88  289 
9.88315 
9.88  341 
9.88  367 
9.88  393 
9.8S  420 
9.S8  446 
9-8S472 


9.88498 


g.bb  524 
9.88  550 
9-88  577 
9.S8  603 
9.88  629 
9.88  655 
9.8S681 
9.88  707 
9-88  733 


9.8S  759 


9.88  786 
9.88  812 
9.88  838 
9.88  864 
9.88  890 
9.88916 
9.88  942 
9.88  968 
9-88  994 


9.89  020 


9.89  046 
9.89073 
9.89  099 

9-89  125 
9-89151 
9.89177 
9.89  203 
9.S9  229 
9-89  255 


9-90235 


0.12  262 
0.12  236 
0.12  210 
0.12  183 
0.12  157 
0.12  131 
0.12  105 
0.12078 
0.12  052 


9.90  225 
9.90  216 
9.90  206 
9.90  197 
9.90  187 
9.90178 
9.90  168 
9.90159 
9-9Q  M9 


0.12  026 


'_).<)0    I  \<, 


o.  1 2  000 
0.11973 
0.1 1  947 
0.11  921 
o.n  S95 
0.1 1  S69 
0.1 1  842 
O.II  S16 
0.1 1  790 


9.90 130 

9.90  120 
9.90  III 
9.90  IOI 
9.90091 
9.90  082 
9.90072 
9.90  063 
9-9°  °53 


o.n  764 


o.n  738 
0.11  711 
o.n  685 
0.11  659 
0.11  633 
0.11  607 
0.11  580 
0.11  554 
o.n  528 


5' '- 


o.n  476 
o.n  450 
o.n  423 

0.11  397 
o.n  371 
o.n  345 
o.n  319 
o.n  293 
o.n  267 


9-89  937 
9.89927 
9.89  918 
9.89  90S 
9.89  898 
9.89  88S 
9.89  879 
9.89  869 
9-89  859 


o.n  241 


9.89  S49 


o.n  214 
0.11  188 
0.11  162 
0.11  136 
0.11  no 
o.n  084 
o.n  058 
o.n  032 
o.n  006 


9.89  840 
9.89  830 
9.89  820 
9.89  810 
9.89  801 
9.89  791 
9.89781 
9.89771 
9.89  761 


9-8g  752 


0.10954 
0.10  927 
0.10901 
0.10875 
0.10  849 
0.10  823 
0.10  797 
0.10  771 
0.10  745 


9.89  742 
9.89  732 
9.89  722 
9.89712 
9.89  702 
9.89  693 
9.89  683 
9.89  673 

9.89  663 


.,.')"  "43 


9.90  034 
9.90024 
9.90014 
9.90  005 
9.89  995 
9.89985 
9.89976 
9.89  966 
9-89  956 


j-89  947 


9.89  28] 


0.10  719 


9-89653 


27 

I 

0.4 

2 

0.9 

3 

1.4 

4 

1.8 

5 

2.2 

6 

2-7 

7 

3-2 

8 

3-6 

9 

4.0 

10 

4-5 

20 

9.0 

30 

13-5 

4" 

18.0 

50 

22.5 

17 

1 

0.3 

2 

0.6 

3 

0.8 

4 

1.1 

5 

M 

6 

1.7 

7 

2.0 

8 

2-3 

9 

2.6 

10 

2.8 

20 

5-7 

30 

8-5 

4" 

"•3 

50 

14.2 

10 

1 

0.2 

2 

0.3 

3 

0.5 

4 

0.7 

S 

0.8 

i. 

1.0 

7 

1.2 

8 

i-3 

9 

1-5 

10 

i-7 

20 

3-3 

30 

5-0 

40 

6.7 

50 

8.3 

26 

0.4 
0.9 

i-3 
i-7 
2.2 

2.6 

3-o 

3-5 

3-9 

4-3 

8.7 

13-0 

17-3 

21.7 

10 

o-3 

0.5 

0.8 

1.1 

1-3 

1.9 
2.1 


5-3 
8.0 


0.4 
0.6 
0.8 
0.9 


i-4 
i-5 
3-0 
4-5 
6.0 
7-5 


10       10 


26 


0 

I 

1.4 

i-3 

4-1 

3-9 

" 

6.8 

6.S 

3 
4 
5 
6 

7 
8 

9-4 

9.1 

12.2 

11. 7 

14.8 

'  !-3 

17.6 

16.9 

20.2 

19-5 

22.9 

22.1 

9 
10 

25.6 

24-7 

LCos 


L  Cot 


(Ml 


LTan 


L  Sin 


I'     V 


442°    232°     *322° 


100 


38c 


*128°    218°    *308° 


il     LCot 


L  Cos 


P    P 


|.B92B1 


9.7S  950 

9.78983 

9.78  999 
9.79015 
9.79031 

9.79  047 
9.79063 
9.79  "79 


)-79  095 


9.79  111 

9.79  128 
9.79  144 
9.79  160 
9.79  176 
9.79  192 
9.79  208 
9.79  224 
9.79  240 


9.79  256 


9.71;  272 
9.79288 
9-79  304 
9-79  319 
9-79  335 
9-79  351 
9-79  367 
9-79  383 
0-79  399 


9-79  41? 


9.79431 

9-79  447 
9-79  463 
9.79  478 

9.79494 
9.79510 
9.79  526 
9-79  542 
9-79  558 


9-79  573 


9-79  589 
9.79605 
9.79621 

9-79  636 
9.79652 
9.79  668 
9.79  684 
9.79699 
9-79  715 


9-79  731 
9-79  74«' 
9-79  762 
9-79  778 
9-79  793 
9-79  809 
9-79  825 
9-79  840 
9-79  856 
9-79  872 


9.89  307 
9-89  333 
9-89  359 
9.89385 
9.89  41  [ 
9-89  437 
9.89  463 
9.89489 
9-89  5I5 


<)->9  ?4i 


9.89  567 

9-89  593 
g.89  619 

9.89  645 
9.89671 
9.89  697 
9.89  723 
9.89  749 
9-89  775 


9.S9  N>| 


9.89  827 

9-89  853 
9.89  879 

9.89  905 
9.8993I 
9-89  957 

9.89  983 

9.90  OO9 

9-9°  °35 


9.90061 


9.90  006 
9.90  112 
9.9O  138 
9.9O  164 
9.9O  I90 
9.9O  2l6 
9.9O  242 
9.90  268 
9-9°  294 


9.91 1  321  > 


9.90346 
9.90371 
9-9°  397 
9.90  423 
9.90  449 
9-90  475 
9-9°  501 
9.90  527 
9-9Q  553 


9-9"  ;7- 


9.90  604 
9.9O  630 
9.9O  656 
9.9O  682 
9.9O  708 
9-9°  734 

9-9°  759 
9.90  785 
9.90811 


9.90  037 


7'9 


9-s9°53 


0.10  693 

0.10  667 
0.10  641 
0.10615 
0.10589 
0.10  563 

0.10537 

0.10  511 
0.10485 


89643 
89633 
89624 

89614 
89  604 

89594 
89584 
89574 
89564 


Q-IQ459 


»9  554 


0.10433 
0.10407 
0.10381 
0.10355 
0.10  329 
0.10303 
0.10  277 
0.10251 
0.10  225 


89  544 
89  534 
89  524 
89  514 
89504 
89495 

89485 
89  475 

89465 


o.io  199 


89455 


0.10  173 
0.10  147 

O.IO  121 
O.IOO95 
O.IO069 
O.IOO43 
O.IOOI7 
O.O9  99I 
0.09  965 


<>■<■*)  939 


89445 
89  435 
89  425 

89  415 
89405 
89  395 
89  385 
89  375 
8g  364 


0.09  914 
0.09  888 
0.09  862 
0.09  836 
0.09  810 
0.09  784 
0.09  758 
0.09  732 
0.09  706 


0.09  680 


0.09  654 
0.09  629 
0.09  603 
0.09  577 
0.09  551 
0.09  525 
'0.09  499 
0.09  473 
009  447 
0.09  422 


n.09  39(1 
0.09  370 
0.09  344 
0.09  318 
0.09  292 
O.og  266 
0.09  241 
0.09  215 
(,.(.()  1  -., 


o.og  [63 


i>9  354 


89  344 
89  334 
89324 
893M 
89304 
89294 
89284 

S9274 
89  264 


254 


^9244 
89233 
89223 

89213 
89203 
89193 
89183 
89  173 
89  102 


89  142 
89  132 

89  122 
89  112 
89  I OI 
89O9] 

8907] 

-,,  060 


Bg  i>5<  1 


26 

I 

0.4 

2 

0.9 

3 

1-3 

4 

i-7 

5 

2.2 

6 

2.6 

7 

3-o 

8 

3-5 

9 

3-9 

10 

4-3 

20 

8-7 

30 

13.0 

40 

17-3 

50 

21.7 

25 

0.4 
0.8 

1.2 

i-7 
2.1 

2-5 
2.9 
3-3 
3-8 
4.2 
8-3 
12.5 
16.7 
20.8 


17 

IB 

I 

0.3 

0.3 

2 

0.6 

0.5 

3 

0.8 

0.8 

4 

1.1 

1.1 

5 

1-4 

1-3 

6 

i-7 

1.6 

7 

2.0 

1.9 

8 

2-3 

2.1 

9 

2.6 

2.4 

10 

2.8 

2.7 

20 

5-7 

5-3 

30 

8.5 

8.0 

40 

H-3 

10.7 

50 

14.2 

13-3 

11 

10 

1 

0.2 

0.2 

2 

0.4 

0.3 

3 

0.6 

0.5 

4 

0.7 

0.7 

5 

0.9 

0.8 

6 

1.1 

1.0 

7 

i-3 

1.2 

8 

i-5 

i-3 

9 

1.6 

i-5 

10 

1.8 

i-7 

20 

3-7 

3-3 

30 

5-5 

5-o 

40 

7-3 

6.7 

SO 

9-2 

8-3 

15 

0.2 
0.5 
0.8 
1.0 
1.2 
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1.8 
2.0 
2.2 
2-5 
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7-5 
1 0.0 
12.5 

9 

0.2 

0.3 

0.4 

0.6 

0.8 

0.9 


1.4 
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3-0 
4-5 
6.0 
7-5 


10 

10 

26 

25 

0 

1  1 

1.2 

2 

3-9 

3-8 

6.5 

6.2 

3 
4 
5 
6 

9.1 
11. 7 

8.8 
11.2 

l  1  -3 

13.8 

16.9 

16.2 

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[9.5 

18.8 

22.1 

21.2 

9 

24.7 

23.8 

26 

1.4 

4-3 
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13-0 
15-9 
18.8 
21.7 

24. (> 


I.  c 


I II 


1.  cot     «•  (I     L  Tan 

^T~        51° 


L  Sin    !  d 


1'     r 


101 


39° 

129°  219°  *309° 

LSin 

(1 

L  Tan  c  d | 

L  Cot 

L  Cos 

d 

P  P 

0 
I 

9.79887 

16 

9.90  837 

26 
26 

0.09  163 

(,.8905(1 

10 

CO 

60 

59 

9.79  903 

9.91  1  S(>3 

0.09  137 

9.89  040 

0.4 

0.9 

i-3 
1.7 

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0.8 

2 

9.79918 

lb 

16 

9.90  889 

25 
26 

0.09  in 

9.89  030 

5« 

2 

3 

3 

9-79  934 

9.90914 

0.09  086 

9.89  020 

57 

4 

9-79  95Q 

9.90  940 

26 

0.09  060 

9.89  009 

5t> 

s 

9-79  965 

15 
16 
15 
16 

9.90  966 

26 

0.09  034 

9.88  999 

55 

5 
6 

2.2 

2.6 

2.1 
2-5 
2.9 
3-3 

6 

9.79981 

9.90  992 

26 

0.09  008 

9.88  989 

1 1 

54 

7 

9.79  996 

9.91  018 

25 
"6 

0.08  982 

9.88978 

53 

7 
8 

3.0 

3-5 

8 

9.80012 

9.91  043 

0.08  957 

9.88968 

52 

9 
10 

9.80027 

16 

15 
1.6 

9.91  069 

26 
26 
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0.08  931 

9.88958 

10 

1 1 

10 

5i 
50 

49 

9 

IO 

20 

3-9 
4-3 
8,7 

3-8 
4.2 
8-3 

9.80  043 

9.91  095 

0.08  905 

9.^  up 

9.80058 

9.9I  121 

0.08  879 

9-8*937 

12 

9.80074 

9.9I  147 

25 
26 

0.08  853 

9.88927 

48 

30 

13.0 

12.5 

13 

9.80089 

x5 
16 

9.9I  172 

0.08  828 

9.88917 

47 

40 

17-3 

[6.7 

14 

9.80  105 

9.9I  I98 

"6 

0.08  802 

9.88  906 

46 

50 

21.7 

20.8 

15 

9.80  120 

1S 
16 

9.9I  224 

26 

0.08  776 

9.88  896 

[0 

45 

16 

9.80  136 

9.91  250 

?6 

0.08  750 

9.88886 

44 

16 

15 

17 

9.80  151 

9.9I  276 

25 
26 

0.08  724 

9.88875 

[0 
[0 

1 1 

III 
10 

43 

1 

0.3 

0.2 

18 

9.80  166 

16 
15 
16 

g.gl  30I 

0.08  699 

9.88  865 

42 

2 

0.5 

0.5 

19 
20 

21 

9.80182 

9.9I  327 

26 

26 

25 

0.08  673 

9.88855 

4i 
40 

39 

3 
4 

5 
6 

0.8 

1.1 

i-3 
1.6 

0.8 
1.0 
1.2 

9.80  197 

9-91  353 

0.08  647 

9.88  844 

9.80213 

9-91  379 

0.08621 

9.88  834 

22 

9.80228 

lS 

16 
15 

15 
16 
15 

15 
16 
15 
15 
16 
15 
15 
16 
15 

9.91  404 

0.08  596 

9.88  824 

38 

i-5 
1.8 
2.0 

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43° 

*133° 

223° 

313 

0 

' 

L  Sin 

cl 

L  Tan  |  c  d  |  L  Cot 

L  Cos  d 

P  P 

0 

T 

9-83378 

9.96  966 

25  - 

0.03  034 

9-86413 

60 

59 

26 

25 

0.4 

9-83  392 

9.96991 

o.i  '3  009 

9.86401 

1 

0.4 

2 

9.83  405 

9.97016 

25 
26 

0.02  984 

9-86389  l 

2  58 

2 

0.9 

0.8 

3 

9.83419 

9.97  042 

0.02  958 

9.86377  l 

2  57 

3 

i-3 

1.2 

4 

9-83  432 

9.97  067 

25 

O.02  933 

9.86  366  r 

1  56 

4 

i-7 

i-7 

5 

9.S3  446 

9.97  092 

25 

O.02  908 

9.86354  1 

2  55 

5 

2.2 

2.1 

6 

9-83  459 

9.97  118 

26 

0.02  882 

9.86  342  1 

2  54 

6 

2.6 

2-5 

7 

9-83  473 

9-97  143 

25 

0.02  857 

9.86  330 

2  53 

7 
8 

3-0 

2.9 

8 

9.83  486 

9.97  168 

25 

0.02  832 

9.86318  x 

52 

3-5 

3-3 
3-8 
4.2 
8-3 
12.5 

9 

10 
ii 

9.83  500 

9-97  193 

25 
26 

25 

0.02  807 

9.86  306  I 

2  5i 
2  49 

9 
10 
20 
30 

3-9 
4-3 
8.7 

13.0 

9-83  5I3 

9.97219 

0.02  781 

9-86295  * 

9-83  527 

9.97  244 

O.02  756 

i)..S(,2S3   ' 

12 

9-83  540 

9.97  269 

25 
26 

0.02  731 

9.86271  r 

2  48 

40 

17-3 

16.7 

13 

9-83  554 

9-97  295 

0.02  705 

9.86259  * 

2  47 

50 

21.7 

20.8 

M 

9.83  567 

9.97  320 

25 

0.02  680 

9.86  247 

2  46 

13 

15 

9.83  581 

9-97  345 

25 

0.02  655 

9-86235  1 

2  45 

Li 

16 

9-83  594 

9-97  371 

26 

0.02  629 

9.S6  223  x 

44 

1 

0.2 

0.2 

17 

9.83  608 

9-97  396 

25 

0.02  604 

9.86  211   * 

43 

2 
3 
4 

5 
6 

7 

O.5 
O.7 
O.g 
1.2 

i-4 
1.6 

0.4 
0.6 

18 

9.83  621 

9.97421 

25 

0.02  579 

9.86  200  l 

1  42 

0.9 

i-3 
i-5 

19 
20 
21 

9-83  634 

9-97  447 

26 
25 
25 
26 

0.02  553 

9..S(,i.^S   ' 

2  4i 
2  40 

:  39 

9.83  648 

9.97472 

0.02  52s 

9.86176  1 

9.83  661 

9-97  497 

0.02  503 

9.86  164 

22 

9.83  674 

9-97  523 

0.02  477 

9.86152   * 

2  38 

8 

1.9 

i-7 

23 

9.83  688 

9-97  548 

25 

0.02  452 

9.86  140   r 

2  37 

9 

2.0 

24 

9-83  701 

9-97  573 

25 

0.02  427 

9.86  128   * 

,  36 

10 

2-3 

2.2 

25 

9-83  7I5 

9-97  598 

25 

0.02  402 

9.86  Il6  1 

2  35 

20 

4-7 

4-3 

26 

9.S3  728 

9.97  624 

26 

0.02  376 

9.86  I04   T 

2  34 

30 

7.0 

6.5 

27 

9.83  741 

9.97  649 

25 

0.02  351 

9.86092 

!  33 

40 

9-3 

8.7 
10.8 

23 

9-83  755 

9-97  674 

25 

0.02  326 

9.86080  l 

2  32 

50 

11. 7 

29 
30 

31 

9.83  768 

9.97  700 

26 

25 
25 
26 

0.02  300 

9.86068  l 

-  31 
29 

11 

0.2 
0.4 

9.83  781 

9-97  725 

0.02  275 

9.86  056 

1 
2 

0.2 
0.4 

9-83  795 

9-97  75o 

0.02  250 

9.86  044 

32 

9.83  808 

9.97  776 

O.02  224 

9.86032  l 

-  28 

3 

0.6 

0.6 

33 

9.83  821 

9.97  801 

25 

0.02  199 

9.86020   : 

0  27 

4 

o.8 

0.7 

34 

9-83  834 

9.97  826 

25 

0.02  174 

9.86008 

"  26 

5 

1.0 

0.9 

35 

9.S3  848 

9.97851 

25 

0.02  149 

9.85996  I 

I  25 

6 

1.2 

1.1 

36 

9.83  861 

9.97877 

26 

0.02  123 

9.85984  J 

\   24 

7 
8 

1.4 
1.6 

1-3 

37 

9.83  874 

9.97  902 

25 

0.02  098 

9.85972 

23 

i-5 
1.6 
1.8 

38 

9.83  887 

9.97927 

25 
26 
25 
25 
26 

0.02  073 

9.85  960 

2   22 

9 
10 
20 
30 
40 

2.0 
4.0 
6.0 

8.0 

39 
40 

4i 

9.83901 

9-97  953 

0.02  047 

9.85  948   j 

2   21 
2  20 

I     r9 

3-7 

5-5 
7-3 

9.83914 

9.97  978 

■  1.1 12  022 

9-85  936 

9.83927 

9.98  003 

0.01  997 

9.85924   ' 

42 

9.83  940 

9.98  029 

0.01  971 

9.85912 

2  18 

50 

1 0.0 

9-2 

43 
44 

9-83  954 
9.83  967 

14 

9.98  054 
9.98  079 

25 

0.01  946 
0.01  921 

9.85  9OO   ] 
9.85  S88  ' 

25 

"  16 

13 

1 

3 

12 

45 

9.83  980 

13 

9.98  104 

25 
26 

O.OI  896 

9.85  876 

2  15 

46 

9-83  993 

13 

9.98  130 

0.01  870 

9.85  864 

3  ;43 

26 

2 

5 

25 

47 

9.84  006 

13 

9-98  155 

25 

0.01  845 

9.85  851 

0 

1.0 

.... 

1.1 

48 

9.84  020 

14 

9.98  180 

25 
26 
25 
25 

0.01  820 

9-85839 

2  12 

1 

3-o 

2.9 

3-1 

49 
50 

51 

9-84033 

13 
13 
13 

9.98  206 

0.01  794 

9-85  827 

[2   IX 

[2  10 
Co   9 

3 
4 
5 
6 

5-o 
7.0 
9.0 

1-8 
'•7 

3-7 

3.6 

5-2 

7-3 
9-4 

9.84  046 

9.98  231 

0.01  769 

9-85815 

9.84059 

9.98  256 

0.01  744 

9.85  S03 

52 

9.84072 

13 

9.98  281 

25 

0.01  719 

9.85  791 

L2    g 

1 1.0 

1 

"•5 

53 

9.84085 

13 

9.98  307 

26 

0.01  693 

9-85  779 

\\          "' 

7 

13-0 

1 

2-5 

13-5 
15.6 
17-7 
19.8 
21.9 

54 

9.84098 

13 

9-98  332 

25 

0.01  668 

9.85  766 

12       6 

8 

15.0 
17.0 
19.0 
21.0 

1 

1 

M 

6-3 
8-3 

0.2 

55 

9.84  112 

14 

9-98  357 

25 
26 

25 

0.01  643 

9-85  754 

ro    5 

9 

56 

9-84  125 

13 
13 

9-98  383 

0.01  617 

9.85  742 

2         4 

10 

2 

57 

9.84  138 

9.98  408 

0.01  592 

9-85  730 

3 

11 

23.0 

2 

2.1 

23-9 

58 

9-84151 

13 

9-9S433 

25 

0.01  567 

9-85718 

■    2 

12 

23.0 

4-1 

59 

.).S4_i()4 

13 

.9.98  458 

25 

26 

0.01  542 

9.85  706 

2   I 

!3 

60 

9-84I77 

13 

9.98  4S4 

0.01  516 

9-85  693 

;  1) 

L  Cos 

cl 

L  Cot 

cd 

L  Tan 

L  Sin  | 

I 

P   P 

*136° 

22(5 

3  *316° 

46° 

106 


uc 


134°     224°     *314< 


LSin 


9-P4  '77 
9.84  190 
9.84  203 
9.84216 
9.84  229 
9.84242 
9-84  255 
9.84  269 
9.84282 
9.84  295 


9.S4  308 
,.84321 
9-84  334 
9-84347 
9.84  360 
9-84  373 
9.84  385 

9.S4  398 
9-84  4II 
9JB4  424 

9-84  437 


9.84450 
9.84  463 
9.84  476 
9.84  489 
9.84  502 
9-84  5I5 
9-84  528 
9.84  540 
9-84  553 


9.84  566 


9.84  579 
9.S4  592 
9.84  605 
9.84618 
9.84  630 
9.84  643 

9-84  656 
9.84  669 
9.84  682 


.84  694 


9.84  707 
9.84  720 
9-84  733 

9-84  745 
9.84  758 

9-84  77I 

9.84  784 

9>4  79'' 
9-N  809 
9-N  822 

9-84  83! 
9.84  847 
9.84  860 
9.84  873 
9.84885 
9.84  898 
9.84911 

9- 84  936 


13 
13 
13 
13 
13 
13 
13 
13 
13 
12 
13 
13 
13 
13 
13 
13 

12 
13 

13 
13 
13 
12 

13 
13 
13 
12 

13 
13 
13 
12 
13 
13 
13 
i  12 
13 
13 
12 
13 
13 
12 
13 
13 


L  Tan   c  d   L  Cot   L  Cos 


9-98  484 


9.98  509 
9-98  534 
9.98  560 

9-98  585 
9.98  610 
9-98  635 
9.98  661 
9.98  686 
9-98  7II 


9-98  737 
9.98  762 
9.98  787 
9.98  812 
9-98  838 
9-98  863 
9.98  888 
9.98913 
9.98  939 
9-9s  964 


9-98  989 
9.99015 
9.99  040 
9.99  065 
9.99  090 
9.99  116 
9.99  141 
9.99  166 
9.99  191 
9-99  217 


9-99  242 


9.99  267 

9-99  293 
9.99318 

9-99  343 

9.99  368 

9-99  394 
9.99419 
9-99  444 

9.99  41.9 


9-99  495 


9.99  520 
9-99  545 
9-99  570 
9.99  596 
9.99  621 
9-99  64*J 
9.99  672 
9.99  697 
9.99  722 


9-99  747 
9-99  773 
9-99  798 
9.99  823 

9.99  848 
9.99874 
9-99  S99 
9-99  924 

9-99  975 


»135  22 


J.  Cot 

»316° 


c  «l 


0.01  516 


0.01  491 
0.0 1  466 
0.0 1  440 
0.01  415 
0.0 1  390 
0.01  365 
0.01  339 
0.01  314 

".(,1  2>9 


0.01  263 


0.01  238 
0.01  213 
O.OI  188 
0.01  162 
0.01  137 

O.OI  112 

0.01  087 
0.01  061 
0.01  036 


O.OI  on 


0.00985 
0.00  960 
0.00935 
0.00910 
0.00  884 
0.00  859 
0.00  834 
0.00  809 
o.oo  783 


0.00  75b 


0.00  733 
0.00  707 
0.00  682 
0.00  657 
0.00  632 
0.00  606 
0.00  581 
0.00  556 
0.00  531 


0.00  505 


0.00480 
0.00455 
0.00  430 
0.00  404 
0.00  379 
0.00  354 
0.00  328 
0.00  303 
0.00  278 


(..(id  253 


0.00  227 
0.00  202 
0.00  177 
0.00  152 
0.00  [26 
0.00  1 01 
0.00  076 
,  1.1  005] 
0.00025 


1  i.(  n 

L  Tan 


().>?  I«h 


9.85  681 

9.85  669 

9-85657 
9.85  645 

9.85  632 
9.85  620 

9.85  608 
9-85  596 

9-85583 


9-85571 


9-85  559 
9-85  547 
9-85  534 
9-85  522 
9-85  5IO 
9-85  497 
9-85  485 
9-85  473 
9.85  460 


9.85448 


9-85  436 
9-S5  423 
9-85411 

9-85  399 
9.S5  386 

9-85  374 
9-85  361 
9-85  349 
9-85  337 


9-85  324 


9-&5  312 
9.S5  299 
9.85287 
9.S5  274 
9.S5  262 
9-85  250 

9-85  237 
9-85225 
9.85212 


9.85  200 


9-85  187 
9-85  175 
9.85  162 

9-85  150 
9-85I37 
9-85  125 
9-85112 
9.85  100 
9.8=  "87 


9.85074 


9.85  002 
9.85  049 
9-85037 
9.85  024 
9.8S  012 

9.84  999 
9.84986 
9-84  974 

9.84  .,49 
L  Sin  1  (I 


P  P 


26 

I 

0.4 

2 

0.9 

3 

I-3 

4 

*-7 

5 

2.2 

6 

2.6 

7 

3-o 

8 

3-5 

9 

3-9 

10 

4-3 

20 

8-7 

30 

13-0 

40 

17-3 

50 

21.7 

26 

0.4 
0.8 


2.1 

2-5 

2.9 

3-3 
3-8 
4.2 
8-3 
12.5 
16.7 
20.8 


14 

13 

I 

0.2 

0.2 

2 

0.5 

0.4 

3 

0.7 

0.6 

4 

0.9 

0.9 

5 

1.2 

1.1 

6 

1.4 

i-3 

7 

1.6 

i-5 

8 

1.9 

i-7 

9 

2.1 

2.0 

10 

2-3 

2.2 

20 

4-7 

4-3 

30 

7.0 

6-5 

40 

9-3 

8.7 

50 

n. 7 

10.8 

12 

0.2 

0.4 
0.6 
0.8 


2.0 
4.0 
6.0 
B.o 

[O.O 


13 

26 

0 

1.0 

3-o 

3 

4 
5 
6 

5-0 

7.0 
9.0 

n.o 
13.0 

8 

9 

0 

1 

15.0 
17.0 
19.0 
21.0 

23.0 

3 

25.0 

12 

26 

0 

j  j 

1 
?. 

3-2 

3 
4 

5 
(» 

5-4 

7.6 
9.8 

1 1.9 

14.1 

8 

16.2 

18.4 

y 

20.6 

22.8 

12 

24.9 

0.9 
2.9 

4.8 
6.7 
8.7 

10.6 

12.5 

14.4 
16.3 
18.3 

20.2 

22.1 
24.I 

12 
25 


3-i 

5-2 

7.3 
9.4 
11.5 

13-5 
15-6 
17-7 
19.8 
21.9 
23-9 


I"  P 


107 


TABLE  OF  THE  NATURAL 

TRIGONOMETRIC  FUNCTIONS 

FROM  MINUTE  TO  MINUTE. 


108 
*90°     180° 


*270 


Naturai 


*91°     181°     *27r 


Sin 

Tan 

Cot 

Cos 

0 

I 

2 

3 

0.1 000 

0.0000 

00 

1. 0000 

60 

59 

5S 
57 

0.0003 
0.0006 
0.0009 

0.0003 

0.0006 
0.0009 

3437-75 
1718.87 

H45-92 

1. 0000 
1. 0000 
1. 0000 

4 

5 
6 

0.0012 
0.0015 
0.0017 

0.0012 
0.0015 
0.0017 

859-436 
6S7.549 
572.957 

1. 0000 
1. 0000 
1. 0000 

56 

55 
54 

7 

S 
9 
10 
ii 

12 

0.0020 
0.0023 
0.0026 

0.0020 
0.0023 
0.0026 

491.106 
429.718 
381.971 

1. 0000 
1. 0000 
1. 0000 

53 
52 
51 
50 
49 

4s 

47 

0.0029 

0.0029 

343-774 

1 .0000 

0.0032 
0.0035 
0.003  S 

0.0032 
0.0035 
0.0038 

312.521 
2S6.47S 
264.441 

1 .0000 
1 .0000 
1 .0000 

14 

J5 
16 

0.0041 
0.0044 
0.0047 

0.0041 
0.0044 
0.0047 

245-552 
229.182 
214.858 

1. 0000 
1. 0000 
1 .0000 

46 

45 
44 

17 
iS 
19 
20 

22 
23 

0.0049 
0.0052 
0.0055 

0.0049 
0.0052 
0.0055 

202.219 
190.9S4 
1S0.932 

1. 0000 
1. 0000 
1 .0000 

43 
42 
4i 
40 

39 

38 
37 

o.oo^S 

0.0058 

171. 8S5 

1 .0000 

0.0061 
0.0064 
0.0067 

0.0061 
0.0064 
0.0067 

163.700 
156.259 

149-4^5 

1. 0000 
1 .0000 
1. 0000 

24 

25 
26 

0.0070 
0.0073 
0.0076 

0.0070 
0.0073 
0.0076 

M3-237 
I37-507 
132.219 

I. 0000 
1. 0000 
1 .0000 

36 
35 
34 

27 
28 
29 
30 

3i 

32 
33 

0.0079 
0.0081 
0.00S4 

0.0079 
0.0081 
0.00S4 

127.321 
122.774 
1 1 S.  540 

1. 0000 
1. 0000 
1 .0000 

33 
S2 
3i 
30 
29 

23 

27 

0.0087 

(....my 

114.589 

1.1  H  H  H , 

0.0090 
0.0093 
0.0096 

0.0090 

0.0093 
0.0096 

110.892 
107.426 
104.171 

1 .0000 
1. 0000 
1. 0000 

34 

35 
36 

37 
38 
39 
40 

41 
42 
43 

0.0099 
0.0102 
0.0105 
0.0108 

O.OIII 

0.01 13 

0.0099 
0.0102 
0.0105 
0.0 1  oS 

O.OIII 

0.0113 

101.107 
98.2179 
95-4895 

92.9085 
90-4633 
88.1436 

1. 0000 
0.9999 
0.9999 
0.9999 
0.9999 
0-9999 

26 
25 
24 

23 
22 
21 
20 

19 

iS 

17 

0.0 1 1 6 

0.0116 

85-9398 

0.9999 

0.01 19 
O.OI22 
0.0125 

0.01 19 
0.0122 
0.0125 

83-8435 
81.8470 
79-9434 

0.9999 
0.9999 
0.9999 

44 
45 
46 

O.OI2S 
0.0131 

0.0134 

0.0128 
0.0131 

0.0134 

78.1263 

76.3900 
74-7292 

0.9999 
O.9999 
0.9999 

16 

15 

47 

4s 

49 

50 

51 
52 
53 

0.0137 
0.0140 

0.0137 
0.0140 
0.0143 

73-I390 
71.6151 

70. 1 533 

0.9999 
0.9999 
0.9999 

13 

10 

9 
s 

0-0145 
0.0148 
o.oi  -  1 
0.0154 

Q.QI45 
0.0148 
O.OI  5 1 
0.0154 

6S.7501 
67.4019 
66.1055 
64.8580 

0.9999 

O.9999 

•'•9999 
0.9999 

54 
55 

56 
57 
• 
59 
60 

"•'"57 
O.OI60 

0.OI66 
O.O169 

"•'"57 
0.0160 
0.0163 
0.0166 
O.OI69 
O.OI72 
O.OI  75 

63-6567 
62.4992 
61.3S29 

59.2659 
5S.2612 

0.9999 
O.9999 
O.9999 
0.9999 
0.9999 
Q-9999 
0.9998 

6 

5 
4 
3 

11 

57.290* 

Cos 

Col 

Tan 

Sin 

Sin 

Tan 

Cot 

Cos 

0 
1 
2 

3 

0.0175 

0.0175 

57.2900 

0.9998 

60 

59 

5S 
57 

0.0177 
0.01  So 
0.01  S3 

0.0177 
0.0 1  So 
0.01  S3 

56.3506 
554415 
54.5613 

0.9998 
0.9998 
0.999S 

4 
5 
6 

0.01S6 
0.0 1 S9 
0.0192 

0.0186 
0.01S9 
0.0192 

53.70S6 
52.SS2I 

52.0S07 

0.9998 
0.999S 
0.999S 

56 
55 
54 

7 
S 
9 

10 
1 1 

13 

0.0195 
0.019S 

0.0201 

0.0195 
0.0198 
0.0201 

51.3032 

50.5485 
49.8157 

0.999S 
0.9998 

0.999S 

53 
52 
5i 
50 

49 
48 
47 

0.0204 

0.0204 

49.1039 

0.9998 

0.0207 
0.0209 
0.0212 

0.0207 
0.0209 
0.0212 

4S.4I2I 

47-7395 
47.0853 

0.999S 
0.999S 
0.999S 

14 

15 

16 

0.0215 
0.0218 
0.0221 

0.0215 

0.0218 
0.0221 

46.44S9 
45.S294 
45.2261 

0.9998 
0.999S 
0.9998 

46 

45 
44 

17 

18 
19 

20 
21 

22 

23 

0.0224 
0.0227 
0.0230 

0.0224 
0.0227 
0.0230 

44.63S6 
44.0661 
43-5oSi 

0.9997 
0.9997 
0.9997 

43 
42 
4i 
40 

39 

38 
37 

0.0233 

0.0233 

42.9641 

0.9997 

0.0236 
0.0239 
0.0241 

0.0236 
0.0239 
0.0241 

42.4335 
41.9158 

41.4106 

0.9997 
0.9997 
0.9997 

24 
25 
26 

0.0244 

0.0247 
0.0250 

0.0244 
0.0247 
0.0250 

40.9174 
40.4358 
39-965! 

o.9997 
0.9997 
0.9997 

36 

35 
34 

27 
28 
29 
30 

31 
32 
33 

0.0253 
0.0256 
0.0259 

0.0253 
0.0256 
0.0259 

39-5059 
39.0568 
3S.6177 

0.9997 
0.9997 
0.9997 

33 
32 
3i 
30 
29 

2S 
27 

0.0262 

0.0262 

38.1885 

0.9997 

0.0265 
0.0268 
0.0270 

0.0265 
0.026S 
0.0271 

37.76S6 

37-3579 
36.9560 

0.9996 
0.9996 
0.9996 

34 
35 
36 

0.0273 
0.0276 
0.0279 

0.0274 
0.0276 
0.0279 

36.5627 
36.1776 
35.S006 

0.9996 
0.9996 
0.9996 

26 
25 
24 

37 
33 

40 

4i 
42 
43 

0.0282 
0.02S5 
0.02SS 

0.02S2 
0.02  S  5 
0.02SS 

35-4313 
35-0695 
34-7I5I 

0.9996 
0.9996 
0.9996 

23 
22 
21 
20 

19 
IS 

0.0291 

0.0291 

34-3673 

0.9996 

0.0294 
0.0297 
0.0300 

0.0294 
0.0297 
0.0300 

34.0273 
33.6935 
33-3662 

0.9996 
0.9996 
0.9996 

44 
45 
46 

0.0302 
0.0305 
0.030S 

0.0303 
0.0306 
0.030S 

33-0452 
32.7303 
32.4213 

0.9995 
0.9995 
0.9995 

16 
15 
14 

47 

4s 

49 
50 

5' 
52 
53 

0.031 1 
0.0314 

0.03 1 7 

0.031 1 
0.0314 

0.0317 

32.1181 
31.S205 
31.5284 

0.9995 
0.9995 
0.9995 

13 
II 

10 

9 

S 

0.0320 

0.0320 

31.2  |ii. 

0.9995 

1  (.0323 
0.0326 
0.0329 

0.0323 
0.0326 
0.0329 

30.9599 
30.6S33 
30.4116 

0.9995 
0.9995 
0.999! 

54 
55 
56 

0.0332 
0.0334 
0.0337 

0.0332 
O.0335 
0.033S 

30.1446 
29.SS23 
29.6245 

0.9995 
0.9994 
0.9994 

6 

5 
4 

57 
5S 
59 
60 

0.0340 
0.0343 
0.0346 

0.0340 
0.0343 

n.<>;,4<> 

29.37]  1 
29.1220 
28.8771 

0.9994 

0.9994 
0.9994 

3 

1 
0 

...•>;  |<i 

0.0349 

2S.6363 

0.9994 

Cos   Col  '  Tan   sin 

9      26fl      »359    Jill 


N   \  Tl    i:  \l. 


*92°  182°  *272° 


9° 


Natural 


100 


■■■VA'    \K>,     *273" 


' 

Sin 

Tan 

Cot 

Cos 

0 

I 

0.0349 

0.0349 

2S.6363 

0.9994 

60 

59 

0.0352 

0.0352 

28.3994 

0.9994 

2 

0.0355 

0.0355 

28.1664 

0.9994 

58 

3 

0.0358 

0.0358 

27.9372 

0-9994 

57 

4 

0.0361 

0.0361 

27.7117 

0.9993 

56 

S 

0.0364 

0.0364 

27.4899 

o.9993 

55 

6 

0.0366 

0.0367 

27-2715 

0.9993 

54 

7 

0,0369 

0.0370 

27.0566 

0.9993 

53 

8 

0.0372 

0.0373 

26.8450 

0.9993 

52 

9 
10 

0.0375 

0.0375 

26.6367 

o.9993 

5i 
50 
49 

0.0378 

0.0378 

26.4316 

0.9993 
o.9993 

0.0381 

0.0381 

26.2296 

12 

0.0384 

0.0384 

26.0307 

o.9993 

48 

13 

0.0387 

0.0387 

25.8348 

0.9993 

47 

14 

0.0390 

0.0390 

25.6418 

0.9992 

46 

IS 

0.0393 

0.0393 

25-45I7 

0.9992 

45 

16 

0.039b 

0.0396 

25.2644 

0.9992 

44 

17 

0.0398 

0.0399 

25.0798 

0.9992 

43 

18 

0.0401 

0.0402 

24.8978 

0.9992 

42 

19 

20 
21 

0.0404 

0.0405 

24.7185 

0.9992 

4i 

40 
39 

0.0407 

0.0407 

24.5418 

0.9992 

0.0410 

0.0410 

24-3675 

0.9992 

22 

0.0413 

0.0413 

24.1957 

0.9991 

38 

23 

0.0416 

0.0416 

24.0263 

0.9991 

37 

24 

0.0419 

0.0419 

23-8593 

0.9991 

36 

25 

0.0422 

0.0422 

23-^945 

0.9991 

35 

26 

0.0425 

0.0425 

23-5321 

0.9991 

34 

27 

0.0427 

0.0428 

23-37i8 

0.9991 

33 

28 

0.0430 

0.0431 

23-2137 

0.9991 

.32 

29 

30 
31 

0.0433 

0.0434 

23-0577 

0.9991 

3i 
30 
29 

0.0436 

0.0437 

22.9038 

0.9990 

0.0439 

0.0440 

22.7519 

0.9990 

32 

0.0442 

0.0442 

22.6020 

0.9990 

28 

33 

0.0445 

0.0445 

22.4541 

0.9990 

27 

34 

0.0448 

0.0448 

22.3081 

0.9990 

26 

35 

0.0451 

0.0451 

22.1640 

0.9990 

25 

36 

0.0454 

0.0454 

22.0217 

0.9990 

24 

37 

0.0457 

0.0457 

21.8813 

0.9990 

23 

38 

0.0459 

0.0460 

21.7426 

0.9989 

22 

39 
40 
4i 

0.0462 

0.0463 

21.6056 

0.9989 

21 
20 
iq 

0.0465 

0.0466 

21.4704 

0.9989 

0.0468 

0.0469 

21.3369 

0.9989 

42 

0.0471 

0.0472 

21.2049 

0.9989 

18 

43 

0.0474 

0.0475 

21.0747 

0.9989 

17 

44 

0.0477 

0.0477 

20.9460 

0.9989 

16 

45 

0.0480 

0.0480 

20.8188 

0.9988 

15 

46 

0.0483 

0.0483 

20.6932 

0.9988 

14 

47 

0.0486 

0.0486 

20.5691 

0.9988 

13 

48 

0.0488 

0.0489 

20.4465 

0.9988 

12 

49 
50 

Si 

0.0491 

0.0492 

20.3253 

0.9988 

11 
10 
9 

0.0494 

0.0495 

20.2056 

0.9988 

0.0497 

0.0498 

20.0872 

0.9988 

52 

0.0500 

0.0501 

19.9702 

0.9987 

8 

53 

0.0503 

0.0504 

19-8546 

0.9987 

7 

54 

0.0506 

0.0507 

19.7403 

0.9987 

6 

55 

0.0509 

0.0509 

19.6273 

0.9987 

5 

5b 

0.0512 

0.0512 

19-5156 

0.9987 

4 

57 

0.0515 

0.0515 

19-4051 

0.9987 

3 

58 

0.0518 

0.0518 

19.2959 

0.9987 

2 

59 
60 

0.0520 

0.0521 

19.1879 

0.99.M) 

0 

0.0523 

0.0524 

19.081 1 

0.9986 

Cos 

Cot 

Tan 

Sin 

' 

Sin 

Tan 

Cot 

Cos 

It 

2 

3 

0.0523 

0.0524 

[9.081  1 

60 

59 

58 
57 

0.0526 
0.0529 
0.0532 

0.0527 
0.0530 
0.0533 

[8.9755 

18.8711 
18.7678 

0.99*6 

4 
5 
6 

0.0535 
0.0538 
0.0541 

0.0536 
0.0539 
0.0542 

18.6656 
18.5645 
18.4645 

0.9986 
O.9986 
0.9985 

56 

55 
54 

7 
8 
9 

10 
11 
12 
13 

0.0544 
0.0547 
0.0550 

0.0544 
0.0547 
0.0550 

18.3655 
18.2677 

1  S.i  708 

0.9985 
O.9985 
0.9985" 

53 
52 
5i 
50 

49 
48 

47 

O.OSV2 

0.0553 

1 8.0751 

O.9985 

O.0555 
O.0558 
O.O561 

0.0556 
0.0559 
0.0562 

17.9802 
17.8863 

17-7934 

O.9985 

0.9984 
0.99S4 

14 

15 
16 

O.0564 
O.0567 
O.O57O 

0.0565 
0.0568 
0.0571 

I7-70I5 
17.6106 
17-5205 

0.9984 
O.998  \ 

0.99-  | 

46 
45 
44 

17 

18 

19 
20 
21 
22 
23 

0.0573 
O.0576 
O.0579 

0.0574 
0.0577 
0.0580 

I7-43I4 
17-3432 

17.2558 

0.9984 
0.9983 
0.9983 

43 
42 
4i 
40 

39 

38 
37 

O.0581 

0.0582 

17-1693 

0-99* 
0.9983 

0.9983 
0.9983 

O.0584 
O.O587 
O.O59O 

0.0585 
0.0588 
0.0591 

17.0837 
16.9990 
16.9150 

24 

25 
26 

O.0593 
O.O596 
O.O599 

0.0594 
0.0597 
0.0600 

16.8319 
16.7496 
16.6681 

0.9982 

0.99.VJ 
0.9982 

36 
35 
34 

27 

28 

29 
30 

31 
32 

33 

0.0602 
O.0605 
O.0608 

0.0603 
0.0606 
0.0609 

16.5874 
16.5075 
16.4283 

0.9982 
0.9982 
0.9982 

33 
32 
3i 
30 

29 

28 

O.061O 

0.0612 

10.3499 

0.9981 

O.0613 
O.0616 
O.0619 

0.0615 
0.0617 
0.0620 

16.2722 
16.1952 
16.1190 

0.9981 
0.9981 
0.99S1 

34 

35 
36 

0.0622 
O.0625 
O.0628 

0.0623 
0.0626 
0.0629 

16.0435 
15.9687 
I5-8945 

0.9981 
0.9980 
0.9980 

26 
25 
24 

37 
38 
39 
40 

41 
42 
43 

O.063I 
O.0634 
O.0637 

0.0632 
0.0635 
0.0638 

15.8211 
I5-7483 
15.6762 

0.9980 
0.9980 

0.9981.) 

23 
22 
21 
20 

19 

18 

0.0640 

0.0641 

15.6048 

0.9980 

O.0642 
O.0645 
O.0648 

0.0044 
0.0647 
0.0650 

I5-5340 
15.4638 
15-3943 

0.9979 

0.9079 
0.9979 

44 
45 
46 

O.065I 
O.0654 
O.0657 

0.0653 
0.0655 
0.0658 

15-3254 
I5-257I 
15.1893 

0.9979 
0.9979 
0.9978 

ii. 
15 
M 

47 
48 
49 
50 

51 

52 

53 

O.0660 
O.0663 
O.0666 

0.0661 
0.0664 

0.01,117 

15.1222 

I5-0557 

14-T'P 

0.9978 
0.9978 
0.9978 

13 
12 
11 
10 

9 

8 

7 

o.o()()() 

0.0670 

I4-9244 

0.9978 

O.067I 
O.0674 
O.0677 

0.0673 
0.0676 
0.0679 

14.859' 

14-7954 
I4.73I7 

"■0977 
0.9977 
0.9977 

54 

55 
56 

O.0680 
O.0683 
O.0686 

0.0682 
0.0685 
0.068  S 

14.6685 
14.6059 
I4-543S 

0.9977 
O.9977 
O.9976 

6 

5 
4 

57 
58 
59 
60 

O.0689 
O.0692 
O.0695 

0.0690 

0.0(H) 3 

0.01)1)0 

14-4823 
14.4212 
14.3607 

0.9976 
1 1.9976 

0.0970 

3 

0 

0.01  „,s 

1  I.O(M)C) 

14.3007  0.9976 

Cos 

Cot 

Tan  |  Sin 

^177°  267°  *357c 


87 


Natural 


8<j 


176°  266°  *35fi° 


110 
*94c     184°     *27t     4° 


Natural 


*95°     185°     *275c 


Sin 

Tan 

Cot 

Cos 

Sin 

Tan 

Cot 

Cos 

0 
I 

3 

( 1.0698 

0.0699 

14.3007 

0.9976 

CO 

59 
58 
57 

0 

2 
3 

0.0S72 

0.0S75 

11.4301 

0.9962 

60 

59 

5S 
57 

0.1  v  1  1 

0.0703 
0.0706 

0.0702 
0.0705 
0.0708 

14.241 1 
14.1S21 
14-1235 

o.9975 
o.9975 
o.9975 

0.0874 
0.0877 
0.0880 

0.0878 
0.0881 
0.08  S4 

11.3919 

"•3540 
11. 3163 

0.9962 
0.9961 
0.9961 

4 

5 
6 

0.0709 
0.0712 
0.0715 

0.071 1 
0.0714 
0.0717 

14.0655 
14.0079 
13-9507 

o.9975 
o.9975 
o.9974 

56 

55 
54 

4 

5 

6 

0.0SS3 
0.08S6 
0.08S9 

0.08S7 
0.0890 
0.0S92 

U.2789 

11.2417 
11.2048 

0.9961 
0.9961 
0.9960 

56 

55 
54 

7 

s 

9 

10 
ii 

13 

0.0718 
0.0721 
0.0724 

0.0720 
0.0723 
0.0726 

13-8940 

13.S378 
13.7S21 

0.9974 
o.9974 
o.9974 

53 
52 
5i 
50 

49 

48 

47 

7 

S 

9 
10 
11 

12 
13 

0.0892 
0.0895 
0.0S98 

0.0S95 
0.0S98 
0.0901 

11.1681 
1 1 . 1 3 1 6 
11.0954 

0.9960 
0.9960 
0.9960 

53 
52 
51 
50 

49 
4S 
47 

0.0727 

0.0729 

13.7267 

o.9974 

0.0901 

0.0904 

11.0594 

0.9959 

0.0729 
0.0732 
0.0735 

0.0731 
0.0734 
0.0737 

13.6719 
13-6174 
13-5634 

0.9973 
o.9973 
0.9973 

0.0903 
0.0906 
0.0909 

0.0907 
0.0910 
0.0913 

11.0237 
10.98S2 
10.9529 

0.9959 
0.9959 
0.9959 

r5 
1 6 

0.0738 
0.0741 

0.0744 

0.0740 
0.0743 
0.0746 

13-5098 
13.4566 
134039 

o.9973 
o.9973 
0.9972 

46 
45 
44 

14 
15 
16 

0.0912 
0.0915 
0.0918 

0.0916 
0.0919 
0.0922 

10.9178 
10.8829 
10.8483 

0.9958 
0.995S 
0.9958 

46 
45 
44 

18 
19 

20 
21 
22 
23 

0.0747 

0.0750 
0.0753 

0.0749 
0.0752 
0.0755 

13-3515 
13.2996 
13.24S0 

0.9972 
0.9972 
0.9972 

43 
42 
4i 
40 

39 
38 

37 

ll 

iS 

J9 
20 
21 
22 
23 

0.0921 
0.0924 
0.0927 

0.0925 
0.0928 
0.0931 

10.8139 
10.7797 
io.7457 

0.9958 
0.9957 
0.9957 

43 
42 
41 
40 

39 
38 
37 

0.0756 
0.0758 
0.0761 
0.0764 

0.0758 

13.1969 

0.9971 

0.0929 

0.0934 

10.7119 

0.9957 

0.0761 
0.0764 
0.0767 

13.1461 

1 3. 09  5  s 

13.0458 

0.9971 
0.9971 
0.9971 

0.0932 
0.0935 
0.093  s 

0.0936 
0.0939 
0.0942 

10.6783 
10.6450 
10.61 18 

0.9956 
0.9956 
0.9956 

24 
25 
26 

0.0767 
0.0770 

0.0773 

0.0769 
0.0772 
0.0775 

12.9962 
1 2.9469 
I2.89SI 

0.9971 
0.9970 
0.9970 

36 

35 
34 

24 
25 
26 

0.0941 

0.0944 
0.0947 

0.0945 

0.094S 
0.0951 

10.5789 
10.5462 
10.5136 

0.9956 
0.9955 
0.9955 

36 
35 
34 

28 
29 
30 

3i 

32 
33 

0.0776 

0.0779 
0.07S2 

0.0778 
0.07S1 
0.07S4 

12.8496 
12.8014 

12.7536 

0.9970 
0.9970 

0.9969 

33 
S2 
31 
30 
29 
28 

27 
28 
29 
30 
31 
32 
33 

0.0950 

0.0953 

0.0956 

0.0954 
0.0957 
0.0960 

10.4813 
10.4491 
10.4172 

0.995! 
0.995! 
0.9954 

33 
32 
3i 
30 
29 

2S 
27 

0.0785 

0.0707 

12.7062 

0.9969 

0.095S 

0.0963 

10.3S54 

0.9954 

.0.07S7 

0.0790 

0.0793 

0.0790 
0.0793 

0.0796 

12.6591 
12.6124 
12.5660 

0.9969 
0.9969 
0.9968 

0.0961 
0.0964 
0.0967 

0.0966 
0.0969 
0.0972 

10.353S 
10.3224 
10.2913 

0.9954 
0.9953 
0.9953 

34 

35 
36 

0.0796 
0.0799 
0.0S02 

0.0799 
0.0S02 
0.0S05 

12.5199 
12.4742 
I2.42SS 

0.9968 
0.9968 
0.9968 

26 

25 
24 

34 
35 
36 

0.0970 

0.0973 

0.0976 

0.0975 
0.097S 
0.0981 

10.2602 
10.2294 
10.1988 

0.9953 
0.9953 
0.9952 

26 
24 

37 
3S 
39 
40 

4i 
42 
43 

0.0S05 
0.0S0S 
0.0S11 

0.0808 
0.0810 
0.0S13 

12.3838 
12.3390 

12.2946 

0.996S 
0.9967 
0.9967 

23 
22 
21 
20 

19 

18 
17 

37 
38 
39 
40 

4i 
42 
43 

0.0979 

0.0982 
0.0985 

0.0983 
0.0986 
0.0989 

10.16S3 
10.1381 
10.10S0 

0.9952 
0.995a 

0.9951- 

23 
21 

20 

19 

iS 

17 

0.0S14 

0.0S16 

12.2505 

0.9967 

0.09S7 

0.0992 

10.07S0 

0.9951 

0.0S16 
0.0S19 
0.0822 

0.08 1 9 
0.0S22 
0.0S25 

12.2067 
12.1632 

12.1201 

0.9967 
0.9966 
0.9966 

0.0990 
0.0993 
0.0996 

0.0995 
0.099S 

O.IOOI 

10.04S3 
10.0187 
9.9893 

0.9951 
0.9951 
0.9950 

44 
45 
46 

0.0S25 
0.0S28 
0.0S31 

0.0S28 
0.0831 
0.0834 

I2.O772 
I2.O346 
II.9923 

0.9966 
0.9966 
0.9965 

16 
15 
14 

44 
45 
46 

0.0999 
0.1002 
0.1005 

0.1004 
0.1007 

O.IOIO 

9.9601 
9.9310 
9.9021 

0.9950 
0.9950 
0.9949 

16 

'5 
14 

47 
48 
49 
50 

5  > 

52 
53 

0.0834 
0.0S37 
0.0840 

0.0837 
0.0S40 
0.0S43 

H.9504 
II.9087 
II.8673 

0.9965 
0.9965 
0.9965 

T3 

1 1 
10 

9 
S 

7 

47 
4S 
49 
50 
51 

0.1008 

O.IOII 

0.1013 

0.1013 
0.1016 
0.1019 

9.8734 
9.8448 

0.KM4 

0.9949 
0.9949 

o.<)<)4<> 

13 
12 
1 1 
10 

9 

8 
7 

0.0843 

0.0S46 

1  l.-.-jl.-J 

.,.,,,,(.4 

0.1016 

0.1022 

<).7**2 

0.Q048 

0.0845 

0.0S48 
0.0851 

0.08  ig 

0.0S51 
0.0S54 

M.7S53 
11.7448 
II.7045 

o.o<  ,OJ 
O.9964 
0.996| 

0.1019 
0.1022 
0.1025 

0.1025 
0.1028 
0.1030 

9.760I 
9.7322 
9.7044 

0.004S 
O.994S 
0.9947 

54 
55 
56 

O.085  ( 
O.0857 

0.0860 

0.0S57 
0.0860 
0.0863 

1 1.6645 
H.6248 
«.5853 

O.9963 
O.9963 

O.9963 

6 

5 
4 

54 
56 

0.102S 
0.1031 
0.1034 

0.1033 

0.1036 

0.1039 

9.676S 
9-6493 
9.6220 

0.9947 
0.9947 
0.9946 

6 

5 
4 

57 
58 
59 
60 

0.0863 

0.0866 
0.0869 
0.0872 

I  ..546. 
11.5073 

II.4685 

O.9963 
0.9963 

1 

0 

^7 
58 
59 
60 

0.1037 
0.11  19 
0.1042 

0.1042 

0.1045 

0.104* 

9-5949 
9.5679 
9.5411 

O.9946 
0.9946 
o.<)()46 

3 
2 

0 

! 

0.0*75 

1  i  |;oi 

0.9963 

i..io}5 

0.1051 

'(■5U4 

0.0045 

Cos 

Cot 

Tan 

Sin 

Cos 

Cot 

Tan 

Sill 

85 


Natural 


!4°*174s    264 


*96°     180c 


Natural 


181 


111 

*277 


Sin  1  Tan 

Cot 

Cos 

0 

I 

0.1045 

0.1051 

9.5144 

0.9945 

60 

59 

0.1048 

0.1054 

9-4*7« 

o.9945 

2 

0.1051 

0.1057 

9.4614 

o.9945 

58 

3 

0.1054 

0.1060 

9-4352 

0.9944 

57 

4 

0.1057 

0.1063 

9.4090 

0.9944 

56 

S 

0.1060 

0.1066 

9-3S3I 

0.9944 

55 

6 

0.1063 

0.1069 

9-3572 

0.9943 

54 

7 

0.1066 

0.1072 

9-3315 

o.9943 

53 

8 

0.1068 

0.1075 

9.3060 

o.9943 

52 

9 
10 
ii 

U.K. ;i 

0.1078 

9.2806 

0.9942 

51 
50 

49 

O.IO74 

0.1080 

9-2553 

....,942 

O.IO77 

0.10S3 

9.2302 

0.9942 

12 

O.IOSO 

0.1086 

9.2052 

0.9942 

48 

13 

O.IO83 

0.10S9 

9.1803 

0.9941 

47 

M 

O.IO86 

0.1092 

9-1555 

0.9941 

46 

15 

O.IO89 

0.1095 

9.1309 

0.9941 

45 

1 6 

O.IO92 

0.1098 

9.1065 

0.9940 

44 

17 

O.IO94 

O.IIOI 

9.0821 

0.9940 

43 

IS 

O.IO97 

0.1104 

9-Q579 

0.9940 

42 

19 
20 

21 

O.I  IOO 

0.1107 

9-0338 

o.9939 

4i 
40 

39 

O.IIO3 

O.IIIO 

9.0098 

0.9939 

O.IIO6 

0.1113 

,S.uS(,o 

o.9939 

22 

0.1 109 

0.1116 

8.9623 

0.9938 

38 

23 

O.I  1 12 

0.1119 

8.9387 

0.9938 

37 

24 

O.III5 

O.II22 

s.9152 

0.9938 

36 

2S 

O.I  1 18 

O.II25 

8.8919 

o.9937 

35 

20 

0.1 1 20 

O.II28 

8.8686 

0.9937 

34 

27 

0.1123 

O.II3I 

8.8455 

o-9937% 

33 

28 

0.1 126 

O.II33 

8.8225 

0.9936 

32 

29 

30 

31 

0.1129 

O.II36 

8.7996 

0.9936 

31 
30 
29 

0.1132 

0.1 139 

8.7769 

0.9936 

O.I  135 

0.1 142 

8.7542 

o.9935 

32 

0.II3S 

0.1145 

8.7317 

0-9935 

28 

33 

0.1141 

0.1148 

8.7093 

o.9935 

27 

34 

0.1 144 

0.1 1 51 

8.6870 

o.9934 

26 

35 

0.1146 

0.1154 

8.6648 

o.9934 

25 

3b 

0.1 149 

0.1157 

8.6427 

o.9934 

24 

37 

0.1152 

0.1 160 

8.6208 

o.9933 

23 

38 

0.1155 

0.1163 

8.5989 

o.9933 

22 

39 
40 

4i 

0.1158 

0.1166 

8.5772 

0.9933 

21 
20 
19 

0.1161 

0.1 169 

8-5555 

0.9932 

0.1164 

0.1172 

8.5340 

0.9932 

42 

0.1 167 

0.1175 

8.5126 

0.9932 

18 

43 

0.1170 

0.1178 

8.4913 

0.9931 

17 

44 

0.1172 

0.11S1 

8.4701 

0.9931 

16 

45 

0.1175 

O.I  1 84 

8.4490 

0.9931 

15 

46 

0.1178 

0.1187 

8.4280 

0.9930 

14 

47 

0.1181 

0.1189 

8.4071 

0.9930 

13 

48 

0.1 184 

0.1192 

8.3863 

0.9930 

12 

49 
50 
SI 

0.1187 

0.1195 

8.3656 

0.9929 

11 
10 
9 

0.1190 

0.1198 

8.3450 

0.9929 

0.1193 

O.I20I 

8.3245 

0.9929 

52 

0.1196 

0.1204 

8.3041 

0.9928 

S 

53 

0.1198 

0.1207 

8.2838 

0.9928 

7 

54 

O.I20I 

O.I2IO 

8.2636 

0.9928 

6 

55 

O.I204 

O.I2I3 

8.2434 

0.9927 

5 

5b 

0.I207 

O.I2I6 

8.2234 

0.9927 

4 

57 

O.I2IO 

O.I2I9 

8.2035 

0.9927 

3 

5» 

O.I2I3 

O.I222 

8.1837 

0.9926 

2 

59 
60 

O.I2I6 

O.I225 

8.1640 

0.9926 

0 

O.I2I9 

O.I228 

8.1443 

0.9925 

Cos  |  Cot  |  Tan 

Sin 

Sin 

Tan    Cot    Cos 

0 

<  >.  1  2  1  1  ) 

O.I22> 

8.1443  1  0.9925 

60 

59 

1 

0.1222 

O.I231 

8.1248 

0.9925 

2 

0.1224 

O.I234 

8.1054 

0.9925 

58 

3 

0.1227 

O.I237 

S.0SO0 

0.9924 

57 

4 

0.1230 

'  1. 1  241 1 

S.0667 

0.9924 

56 

5 

0.1233 

O.I243 

8.O476 

0.9924 

55 

6 

0.1236 

O.I240 

8.O285 

0.9923 

54 

7 

0.1239 

O.I249 

8.OO95 

0.9923 

53 

S 

0.1242 

O.I25I 

7.9906 

0.9923 

52 

9 
10 

0.1245 

O.I254 

7-')7's 

"MM-"-' 

5i 
50 

49 

< ..  1 2  1  - 

O.I257 

7-9530 

'  1.9922 

0.1250 

O.I260 

7-9344 

O.9922 

12 

0.1253 

O.I263 

7.9158 

O.992I 

48 

13 

0.1256 

O.I266 

7-8973 

O.992I 

47 

14 

0.1259 

O.I269 

7.8789 

O.992O 

4" 

IS 

0.1262 

O.I272 

7.S60O 

0.9920 

45 

16 

0.1265 

O.I275 

7.8424 

O.992O 

44 

17 

0.1268 

O.I278 

7.8243 

0.99I9 

43 

iS 

0.1271 

O.I28I 

7.8062 

O.99I9 

42 

*9 
20 

0.1274 

O.I284 

7.7882 

0.1,919 

41 
40 
39 

0.1276 

O.I287 

7-7704 

0.1 ,9'  s 

0.1279 

O.I29O 

7-7525 

1  1.99  1  S 

22 

0.1282 

O.I293 

7.7348 

O.99I7 

38 

23 

0.1285 

O.I296 

7-7I7I 

O.99I7 

37 

24 

0.1288 

O.I299 

7.6996 

0.9917 

36 

2^ 

0.1291 

O.I302 

7.6821 

O.9916 

35 

26 

0.1294 

O.I305 

7.6647 

1  1.9916 

34 

27 

0.1297 

O.I308 

7-6473 

0.99 1 6 

33 

28 

0.1299 

O.I3II 

7.6301 

O.9915 

32 

29 

30 
31 

0.1302 

O.I3I4 

7.6129 

0.9915 

3i 
30 

29 

0.1305 

O.I3I7 

7.5958 

0.9914 

0.1308 

O.I3I9 

7-5787 

0.9914 

32 

0.1311 

O.I322 

7.5618 

O.9914 

28 

33 

0.1314 

O.I325 

7-5449 

0.9913 

27 

34 

0.1317 

O.I328 

7.5281 

0.9913 

26 

35 

0.1320 

O.I33I 

7-5II3 

0.9913 

25 

36 

0.1323 

O.I334 

7-4947 

0.9912 

24 

0.1325 

O.I337 

7.4781 

0.9912 

23 

38 

0.1328 

O.I340 

7.46I5 

0.991 1 

22 

39 
40 

4i 

0.1331 

O.I343 

7-4451 

o.MMl  1 

21 

20 
19 

0.1334 

O.I346 

7.4287 

o.MMl  I 

o.i337 

O.I349 

7.4124 

O.99IO 

42 

0.1340 

O.I352 

7-3962 

o.MMl" 

18 

43 

0.1343 

O.I355 

7.3800 

O.99O9 

17 

44 

0.1346 

O.I358 

7-3639 

O.99O9 

16 

45 

0.1349 

O.I361 

7-3479 

O.99O9 

15 

46 

0.1351 

O.I364 

7-3319 

O.99O8 

'4 

47 

0.1354 

O.I367 

7.3l6o 

O.9908 

13 

48 

0.1357 

O.I370 

7.3002 

O.99O7 

12 

49 
50 

51 

0. 1 360 

O.I373 

7.2844 

O.99O7 

1  1 
10 

9 

0.1363 

O.I376 

7.26S7 

O.99O7 

0.1366 

0.137,, 

7-2531 

O.99O6 

52 

0.1369 

O.I3S2 

7-2375 

O.99O6 

S 

53 

0.1372 

O.I38! 

7.2220 

O.99O5 

7 

54 

o.i374 

O.I388 

7.2066 

O.99O5 

6 

55 

0.1377 

0.1391 

7.1912 

0.9905 

5 

56 

0.1380 

O.I394 

7-1759 

O.99O4 

4 

57 

0.1383 

O.I397 

7.1607 

O.99O4 

3 

58 

0.1386 

0.1399 

7-1455 

O.99O3 

2 

59 
60 

0.1389 

0.1402 

7.1304 

1  1.9903 

0 

0.1392  |  0.1405 

7.1 1 54  |  -.mm-;. 

Cos  |  Cot 

Tan    Sin 

' 

173'     263°     *353°  83c 


Natural 


172°     262 


*352 


112 

*98°     188°  *278e 


Natural 


QO        *ggo      j^go   *2790 


sin   Tan   Cot 

Cms 

0 

2 

3 

0.1392  |  0.1405 

7.II54 

0.9903 

60 

59 
58 

57 

0.1395  0.1408 

0.1411 

0.14* .1414 

7.I004 
7.0S55 
7.0706 

■  1.9902 
0.9902 
0.9901 

4 
5 
6 

0.1409 

0.1417 
0.1420 
0.1423 

7.0558 
7.04I0 
7.0264 

0.9901 

■  >.<)<)<  1 

().<)(  )<  ,11 

56 

55 

54 

7 
8 

9 

Hi 
1 1 

12 

13 

0.1412 
0.1415 
0.1418 

0.1426 
0.1429 
0.1432 

7-OH7 
6.9972 
6.9827 

|  |.QQ(  ,1  , 

M.'|>99 
O.9899 

53 
52 
5i 
50 

49 

4  s 
47 

0.1421 

O.M35 

6.9682 

O.9899 

0.1423 
0.1426 
0.1429 

...143S 
"•'44' 
0.1444 

6.9538 

6-9395 
6.9252 

0.98,, 8 
O.9898 
O.9897 

14 
15 
16 

0.1432 
0.1435 
0.1438 

0.1447 
0.1450 
O.I453 

6.91 10 
6.8969 
6.8828 

O.9897 
O.9897 
O.9896 

46 

45 
44 

17 
18 
19 
20 

23 

0.1 441 
O.I444 
0.1446 

0.1456 
0.1459 
0.1462 

6.8687 
6.8548 
6.8408 

O.9896 
O.9895 
O.9895 

43 
42 
4i 
40 

39 

3S 
37 

0.1449 

0.1465 

6.8269 

O.9894 

0.1452 
O.I455 
0.1458 

0.1468 
0.1471 
0.1474 

6.8131 
6-7994 
6.7856 

O.9894 
O.9894 
O.9893 

24 

25 
26 

0.1461 
0.1464 
0.1467 

0.1477 
0.1480 
0.1483 

6.7720 

6.7584 
6.7448 

O.9893  * 

O.9892 

O.9892 

36 
35 
34 

27 
28 
29 
30 

3i 

32 

33 

0.1469 
0.1472 
0.1475 

0.1486 
0.1489 
0.1492 

6.7313 
6.7179 

6.7045 

O.989I 
O.989I 
O.989I 

33 
32 
31 
30 

29 

28 

27 

0.147.-  ! 

6.6912   0.9890 

o.1 48 1 

0.1484 
0.1487 

0.1497 
0. 1 500 
0.1503 

6.6779 
6.6646 
6.6514 

O.9S9O 

M.,,SS(, 

0.9889 

34 
35 
36 

0.1490 
0.1492 
0.1495 

0.1506 
0.1509 
0.1512 

6.6383 
6.6252 
6.6122 

0.9888 
0.9888 
0.9888 

26 
25 
24 

37 
38 
39 
40 

41 

42 
43 

0.1498 
0.1501 

0. 1  5M4 

0-I515 
0.1518 
0.1521 

6.5992 

6.5S63 
6-5734 

0.9887 
0.9887 
0.9886 

23 

20 

19 
18 
17 

0.1507 

0.1524 

6.5606 

0.9886 

O.1510 
O.I5I3 
O.I5I5 

0.1527 
0.1530 
0-I533 

6.5478 
6.5350 
6.5223 

0.9885 
0.9885 
0.9884 

44 
45 
46 

O.1518 
O.1521 
O.1524 

0.1536 

O.I539 

0.1542 

6.5097 
6.4971 
6.4846 

0.9884 
0.9884 

0.9883 

16 

1 5 

'4 

47 

48 
49 

50 

51 

52 

53 

O.1527 
O.1533 

O.I545 
0.1548 
0.1551 

6.4721 
6.4596 
6.4472 

0.9883 
0.9882 
0.9882 

13 
12 
II 
10 

9 

8 

O.I536 

0-I554 

6.4348 

0.9881 

0.1538 
O.154] 

0-I544 

O.I557 

M.I  56O 
0.1563 

6.4225 
6.4103 

(>.  *<)Sm 

M..,SSl 

o.qSSo 
O.9880 

54 
55 
56 

0.1  547 

"■'553 

0.1566 
0-I56g 
0.1572 

6.3859 
6-3737 
6.3617 

O.9880 
O.9879 
O.9879 

6 

5 
4 

57 

- 

59 

O.I575 
O.I578 

-I   -  1 

6.3496 
6.3376 
6.3257 

O.9878 
O.9878 
0.9877 

3 

1 

m 

l   1 

0.1584 

0.9877 

11 

|  Cos   Col   Tan   Sin  | 

Sin  i  Tan  |  Cot 

Cos 

0 

1 

3 

0.1564  |  0.1584 

6.3138 

o.T77 

60 

59 

58 
57 

0.1567 
0.1570 
O.I573 

0.1587 
0.1590 
O.I593 

6.3019 
6.2901 
6.2783 

0.9876 
0.9876 
0.9876 

4 

5 
6 

0.1576 
0.1579 
0.1582 

0.1596 
0.1599 

0.1602 

6.2666 
6.2549 
6.2432 

0.9875 
0.9875 
0.9874 

56 

55 
54 

8 

9 

10 

12 

0.1584 
0.1587 

M.I?UO 

0.1605 
0.1608 

0.161  1 

6.2316 
6.2200 
6.20S5 

0.9874 
0.9873 
0.9873 

53 
52 
5i 

50 

49 
48 

47 

0.15., 3 

0.1614 

6.1970 

0.9872 

0.1  59(1 
0.1599 
0.1602 

0.1617 
0.1620 
0.1623 

6.1856 
6.1742 
6.1628 

0.9872 
0.9871 
0.9871 

14 
15 
16 

0.1605 
0.1607 
0.1610 

0.1626 
0.1629 
0.1632 

6.1515 
6.1402 
6.1290 

0.9870 
0.9870 
0.9869 

46 

45 
44 

19 

20 

21 
22 

23 

0.1613 
0.1616 
0.1619 

0.1635 
0.1638 

M.  K14I 

6.1178 
6.1066 

6.0955 

O.9869 

0.9869 
0.9868 

43 
42 
41 
40 

39 
38 
37 

0.1622 

O.I644 

6.0844 

0.9868 

0.1625 
0.1628 
0.1630 

O.I647 
O.I65O 
O.I653 

6.0734 
6.0624 
6.0514 

0.981)7 
0.9867 
0.9866 

24 
25 
26 

0.1633 
0.1636 
0.1639 

O.I655 
O.I658 
O.I66I 

6.0405 
6.0296 
6.0188 

0.9866 
0.9865 
0.9865 

36 

35 
34 

27 
28 
29 
30 

31 
32 
33 

0.1642 
0.1645 
0.1648 

O.I664 
O.I667 
O.I67O 

6.0080 
5.9972 
5.9865 

0.9864 
0.9864 

33 
32 
31 

30 
ag 

28 
27 

d.ll,;,, 

O.I673 

5-9758 

M.,,.M.3 

O.I653 
O.1656 
O.1659 

O.I676 

O.I679 
O.I682 

5.9651 
5-9545 
5-9439 

0.9862 

0.9862 
0.9861 

34 
35 
36 

O.I662 
O.1665 
O.I668 

O.I685 
O.I688 
O.I69I 

5-9333 
5.9228 
5.9124 

0.9861 

0.9860 
0.9860 

20 
25 
24 

37 
38 
39 
40 

4i 

42 
43 

O.167I 
O.I673 
O.1676 

O.I694 
O.I697 
O.I700 

5.9019 
5.8915 
5.8811 

0.9859 

0.9859 

M.-P5,, 

23 

20 

19 

18 

17 

•'.I67., 

O.I703 

5.8708 

0.1)858 

O.I682 
O.1685 
O.I688 

O.I706 
O.I709 
O.I7I2 

5.8605 
5.8502 
5.8400 

0.9858 
0.9857 
O.9857 

44 
45 
46 

O.169I 
O.1693 
O.1696 

O.I7I5 

0.1 71 8 
0.1721 

5.8298 
5.8197 
5.8095 

0.9856 
0.9856 
0.9855 

16 
15 
14 

47 
48 
49 
50 

5i 
1  52 

53 

0.  1  "')'! 
O.I702 
O.I705 

0.1724 
0.1727 

".173" 

5-7994 
5.7894 

5-7794 

0.9855 
O.9854 

13 
12 

10 

9 

8 

M.I  70S 

m.i  733 

5-7694 

0.9853 

M.|  7M 

0.1714 
0.1716 

m.i73<> 

O.I739 

0.1742 

5-7594 
5-7495 

5.7396 

O.9853 
0.9852 
0.9852 

54 
55 
56 

0.1719 
0.1722 
0.1725 

O.I745 
0.1748 
0.1751 

5-7297 
5.7199 

5-7101 

0.(1851 
O.985] 

M.(|>5<' 

6 

4 

57 
5  s 
5o 
60 

0.1728 
0.173] 

0.1734 
0.1736 

"•'754 
"•'757 
0.17(H) 

O.1763 

5.7004 
5.6906 

5.0S0C) 
5.6713 

0.9850 
0.9849 

0.9S49 

3 
2 

1 

0 

Cos    Cot  |  Tan 

Sin 

171    _i;i      851 


81' 


\  \  1  ri:  \i 


80c 


170    260      350 


*100°  190°  *280°       10° 


Natural 


ir 


*101°  191* 


na 

'281° 


Sin  |  Tan 

Cot 

Cos 

0 

2 

3 

0.1736 

0.1763 

5-6713 

n.ip  p 

60 

59 
58 
57 

0.1739 
0.1742 

0.1745 

0.1  766 
O.1769 
O.1772 

5- 
5- 
5- 

6617 
6521 
6425 

O.9848 
O.9847 
0.9847 

4 
5 
6 

0.1748 
0.1751 
0.1754 

O.I775 
O.1778 
O.1781 

5- 
5- 
5- 

6329 
6234 
6140 

O.9846 
O.9846 
O.9845 

56 
55 
54 

7 

8 

9 
10 

ii 

13 

0.1757 
0.1759 
0.1762 

O.1784 
O.1787 
O.179O 

5- 

5- 
5 

6045 
595i 

5857 

O.9845 
O.9844 

o.()S43 

53 
52 
5i 
50 
49 
4S 
47 

0.1765 

O.I793 

5 

5  7<>4 

0.9S43 

0.17C.S 
0.1771 
0.1774 

c.i  796 

0.1799 

0.1802 

5 
5 
5 

5671 

5578 
5485 

0.9842 
0.9842 
0.9841 

14 

15 
16 

0.1777 
0.1779 
0.1782 

0.1805 
0.1808 
0.1811 

5 
5 
5 

5393 
530I 
5209 

0.9841 
0.9840 
0.9840 

46 
45 
44 

17 
18 
19 
20 
21 

23 

0.1785 
0.1788 
0.1791 

0.1814 

0.1817 
0.1820 

5 
5 
5 

5118 
5026 
4936 

0.9839 
0.9839 
0.9838 

43 
42 
41 
40 

39 

38 
37 

0.1794 

0.1823 

5 

4845 

0.9838 

0.1797 
0.1799 
0.1802 

0.1826 
0.1829 
0.1832 

5 
5 
5 

4755 
4665 
4575 

0.9837, 
0.9837 
0.9836 

24 

25 
26 

0.1805 
0.1808 
0.1811 

0.1835 

0.1838 
0.1841 

5 
5 
5 

4486 
4397 
4308 

0.9836 
O.9835 
O.983! 

36 

35 
34 

27 
28 
29 
30 
31 
32 
33 

0.1814 
0.1817 

0.1819 

0.1844 
0.1847 
0.1850 

5 
5 
5 

4219 
4131 

4043 

0.9834 
0.9834 

0.9S33 

33 

32 
3i 
30 
29 

28 
27 

0.1S22 

0.1853 

5 

39S  5 

0-9833 

0.1825 
0.1828 
0.1831 

0.1856 
0.1859 
0.1862 

5 
5 
5 

38(>s 
•3781 
•3694 

0.9832 
0.9831 
0.9831 

34 
35 
36 

0.1834 
0.1837 
0.1840 

0.1865 
0.1868 

0.1871 

5 
5 
5 

.3607 
•3521 
•3435 

0.9830 
0.9830 
0.9829 

26 

25 
24 

37 
38 
39 
40 
41 
42 
43 

0.1842 
0.1845 
0.1848 

0.1874 
0.1877 

0.1880 

5 
5 
5 

•3349 
•3263 

•3178 

0.9829 
0.9828 
0.9828 

23 
22 
21 
20 

19 

18 
17 

0.1851 

0.I.SS3 

5 

■3093 

0.9827 

0.1854 
0.1857 
0.1860 

0.1887 

0.1890 
0.1893 

5 
5 
5 

.3008 
.2924 
.2839 

0.9827 
0.9826 
0.9826 

44 
45 
46 

0.1862 
0.1865 
0.1868 

0.1896 
0.1899 
0.1902 

•2755 
.2672 
.2588 

0.9825 
0.9825 
0.9824 

16 

15 

47 

48 

49 
50 

51 

52 
53 

0.1871 
0.1874 
0.1877 

0.1905 
0.1908 
0.1911 

•2505 
.2422 
•2339 

0.9823 
0.9823 
0.9822 

13 
12 
11 
10 

9 

8 
7 

0.1880 

0.1914 

•2257 

0.9822 

0.1882 
0.1885 
0.1888 

0.1917 

0.1920 
0.1923 

.2174 
.2092 
.2011 

0.9821 
0.9821 
0.9820 

54 
55 
56 

0.1891 
0.1894 
0.1897 

0.1926 
0.1929 
0.1932 

.1929 

.1848 
.1767 

0.9820 
0.9819 
0.9818 

6 

5 
4 

57 
58 
59 
60 

0.1900 
0.1902 
0.1905 

0.1935 

0.1938 
0.1941 

.1686 
.1606 
.1526 

0.9818 
0.9817 
0.9817 

3 
2 
1 
0 

0.1908 

0.1944 

: 

.1446 

0.9816 

Cos 

Cot 

Tan 

Sin 

Sin  J  Tan    Cot 

Cos 

0 

O.  [90S 

O.I944 

5.3  |,'' 

60 

59 

-.I')l  1 

0.1947 

5.1366 

0.9E  16 

2 

O.I9I4 

0.1950 

5.1286 

58 

3 

O.I9I7 

O.I953 

5.1207 

0.9815 

57 

4 

0.1920 

0.1956 

5.1128 

0.9814 

56 

5 

O.I922 

O.I959 

5.1049 

O.981  ) 

55 

6 

O.I925 

0.1962 

5.0970 

0.9813 

54 

7 

O.I928 

0.1965 

5.0892 

0.0-1  2 

53 

8 

O.I93I 

0.1968 

5-0814 

o.ijSi-j 

52 

9 
10 

1 1 

O.I934 

0.1971 

>"73<< 

0.9K.1  1 

51 
50 

49 

0.1937 

O.I974 

5-0658 

0.9S]  1 

O.IO.V) 

"•"(77 

5.0581 

".,,-  10 

12 

<).I(j42 

0.1980 

5-0504 

O.9810 

48 

13 

O.I945 

0.1983 

5-042  7 

O.9809 

47 

14 

O.I948 

0.1986 

5-0350 

O.9808 

46 

15 

O.I95I 

0.1989 

5-0273 

O.9808 

45 

>."' 

O.I954 

0.1992 

5-0197 

O.9807 

44 

17 

O.I957 

0.1995 

5.0121 

O.9807 

4.1 

18 

O.I959 

0.1998 

5  -004  5 

42 

19 
20 
21 

O.I962 

0.2001 

4.9001, 

O.9806 

4i 
40 

39 

O.I965 

0.2004 

4.9894 

0.0S05 

O.I968 

0.2007 

4.9819 

0.9N1  i 

22 

O.I97I 

0.2010 

4.9744 

O.9804 

.38 

23 

O.I974 

0.2013 

4.9669 

O.9803 

37 

24 

O.I977 

0.2016 

4-9594 

O.9803 

36 

25 

O.I979 

0.2019 

4-952o 

O.9802 

35 

26 

O.I982 

0.2022 

4.9446 

O.9802 

34 

27 

O.I985 

0.2025 

4-9372 

O.980I 

33 

28 

O.I988 

0.2028 

4.9298 

O.980O 

32 

29 
30 
31 

O.I99I 

0.2031 

4.9225 

O.980O 

31 
30 

O.I994 

0.2035 

4.9152  0.9799 

O.I997 

0.2038 

4.9078 

0.9799 

32 

O.I999 

0.2041 

4.9006 

O.9798 

28 

33 

0.2002 

0.2044 

4-8933 

O.9798 

27 

34 

0.2005 

0.2047 

4.8860 

O.9797 

26 

35 

0.2008 

0.2050 

4.8788 

O.9796 

25 

36 

0.20I  I 

0.2053 

4.8716 

O.9796 

24 

37 

0.20I4 

0.2056 

4.8644 

0.9795 

23 

38 

0.20I6 

0.2059 

4-8573 

0.9795 

22 

39 
40 

41 

0.20I9 

0.2002 

4.8501 

O.9794 

21 

20 
19 

0.2022 

0.2065 

4.8430 

0.9793 

0.2025 

0.2068 

4-8359 

0.9793 

42 

0.2028 

0.2071 

0.9792 

IS 

43 

0.203I 

0.2074 

4.8218 

0.9792 

17 

44 

0.2034 

0.2077 

4.8147 

O.979I 

16 

45 

O.2O36 

0.2080 

4-8077 

O.979O 

15 

4b 

0.2039 

0.2083 

4.8007 

O.979O 

14 

47 

0.2042 

0.2086 

4-7937 

O.9789 

13 

48 

0.2045 

0.2089 

4.7867 

O.9789 

12 

49 
50 
51 

0.2048 

o.2(i()2 

4.7798 

O.9788 

1 1 
10 
9 

0.205I 

0/J095 

4-7729 

O.9787 

0.2054 

O.2098 

4-7659 

O.9787 

52 

0.2056 

0.2IOI 

4-7591 

8 

53 

0.2059 

0.2I04 

4.7522 

O.9786 

7 

54 

0.2062 

0.2I07 

4-74  =  3 

O.9785 

6 

55 

0.2065 

0.2I  IO 

5 

56 

0.2068 

0.2II3 

4-7317 

0.9784 

4 

57 

0.207I 

0.2II6 

4-7249 

0.9783 

3 

58 

0.2073 

O.2II9 

4.7181 

O.97S3 

2 

59 
60 

0.2076 

0.2I23 

4.7114 

O.9782 

1 
0 

0.2079 

•  i.2I2() 

4.7041 

..,,"-: 

Cos 

Cot   Tan 

Sin 

*169°  259°  *349c 


79c 


Natural 


78 


►168    258°  *348° 


114 
*102°  192°  *282c 


12° 


Natural 


13c 


'103°  193°  *283° 


Sin 

Tan 

Cot 

Cos 

Sin 

Tan 

Cot 

Cos 

0 

I 

2 

3 

0.2079 

0.2126 

4.7046 

0.9781 

60 

59  v 

58 
57 

0 

1 
2 
3 

0.2250 

0.2309 

4-3315 

0.9744 

60 

59 

58 

57 

0.2082 

0.2085 
0.2088 

0.2129 
0.2132 
0.2135 

4.6979 
4.6912 

4-6845 

0.9781 
0.9780 
0.9780 

0.2252 
0.2255 
0.2258 

0.2312 
0.2315 
0.2318 

4-3257 
4.3200 
4-3143 

0.9743 
0.9742 
0.9742 

4 
5 
6 

0.2090 
0.2093 
0.2096 

0.2138 
0.2141 
0.2144 

4.6779 
4.6712 
4.6646 

0.9779 
0.9778 
0.9778 

56 

55 
54 

4 
5 
6 

0.2261 
0.2264 
0.2267 

0.2321 
0.2324 
0.2327 

4.3086 
4.3029 

4.2972 

0.9741 
0.9740 
0.9740 

56 

55 
54 

8 
9 
10 
ii 

13 

0.2099 
0.2102 
0.2105 

0.2147 
0.2150 
0.2153 

4.6580 
4.6514 

4-644$ 

0-9777 
0-9777 
0.9776 

53 
52 
5i 
50 

49 
48 
47 

8 
9 

10 
11 

13 

0.2269 
0.2272 
0.2275 

0.2330 
0.2333 
0.2336 

4.2916 
4.2859 

4.2-03 

0-9739 
0.9738 
0.9738 

53 
52 
51 
50 

49 

4S 
47 

0.2108 

M.2  1  5(1 

4.1.3*2 

0-9775 

0.2278 

0.2339 

4-2747 

0-9737 

(1.21  I" 
0.2II3 
0.2II6 

C2I59 
0.2I62 
O.2165 

4-63I7 
4.6252 
4.6187 

0-9775 
0-9774 
0-9774 

0.2281 
0.2284 
0.2286 

0.2342 
0.2345 
0.2349 

4.21,01 
4-2635 
4.2580 

0.9736 
0.9736 
0.9735 

14 
16 

O.2II9 
0.2I22 
0.2I25 

0.2168 
0.2I7I 
O.2174 

4.6122 
4-6057 
4-5993 

0-9773 
0.9772 
0.9772 

46 

45 
44 

15 
16 

0.2289 
0.2292 
0.2295 

0.2352 
0.2355 
0.2358 

4.2524 
4.2468 
4-2413 

o.9734 
o.9734 
o.9733 

46 
45 
44 

17 

iS 

19 
20 

21 

22 

23 

0.2I27 
0.2I30 
0.2I33 

0.2I77 
0.2I80 
O.2183 

4.5928 
4.5864 
4.5800 

0.9771 
0.9770 
0.9770 

43 
42 
4i 
40 

39 

38 

37 

17 
18 
*9 
20 
21 
22 
23 

0.2298 
0.2300 
0.2303 

0.2361 
0.2364 
0.2367 

4.2358 
4.2303 
4.2248 

0.9732 
0.9732 
0.9731 

43 
42 

4i 
4(> 

39 

3S 
37 

O.2136 

0.2I86 

4-5736 

0.9769 

0.2306 

0.2370 

4-2193 

0.9730 

O.2139 
0.2I42 
0.2I45 

O.2189 
O.2193 
O.2I96 

4-5673 
4.5609 
4-5546 

0.9769 
0.9768 
0.9767 

0.2309 
0.2312 
0.2315 

0.2373 
0.2376 
0.2379 

4-2139 
4.2084 
4.2030 

0.9730 
0.9729 

0.972s 

24 

25 
26 

0.2I47 
0.2I50 
0.2I53 

O.2I99 
0.2202 
0.2205 

4-54S3 
4.5420 
4-5357 

0.9767 
0.9766 
0.9765 

36 
35 
34 

24 
25 
26 

0.2317 
0.2320 
0.2323 

0.2382 
0.2385 
0.2388 

4.1976 
4.1922 
4.1868 

0.9728 
0.9727 
0.9726 

36 

35 

34 

27 

28 

29 

30 
31 

32 

33 

O.2I56 
0.2I59 
0.2I62 

0.2208 
0.22II 
O.2214 

4-5294 
4-5232 

4.5169 

0.9765 
0.9764 

0.9764 

33 
32 
3i 

30 

29 
28 
27 

27 
28 
29 
30 

31 
32 

33 

0.2326 
0.2329 

0.2332 

0.2392 
0-2395 

0.2398 

4.1S14 
4.1760 
4.1706 

0.9726 
0.9725 

0.9724 

33 

32 
3i 
30 

29 

28 
27 

0.2K14 

0.2217 

4.5107 

0.9763 

0.2334 

0.2401 

4.1653 

0.9724 

O.2167 
O.2I70 
0.2I73 

0.2220 
0.2223 
0.2226 

4-5045 
4.49S3 
4.4922 

0.9762 
0.9762 
0.9761 

0.2337 
0.2340 
0.2343 

0.2404 
0.2407 
0.2410 

4. 1 600 
4-1547 
4-M93 

0.9723 
0.9722 
0.9722 

34 
35 
36 

O.2176 
O.2I79 
0.2l8l 

O.2229 
O.2232 
0.2235 

4.4860 
4-4799 
4-4737 

0.9760 
0.9760 
0-9759 

26 
25 
24 

34 
35 
36 

0.2346 
0.2349 
0.2351 

0.2413 
0.2416 
0.2419 

4-M4I 
4-1388 
4.1335 

0.9721 
0.9720 
0.9720 

26 
25 
24 

37 
38 
39 
40 
4i 
42 
43 

O.2184 
0.2I87 

0.2  I  ( )ii 

O.2238 
O.224I 
O.2244 

4.4676 
4.4615 

4-4555 

0-9759 
0.9758 
0-9757 

23 
22 
21 
20 

19 

iS 

17 

37 
38 
39 
40 
41 
42 
43 

0.2354 
0.2357 
0.2360 

0.2422 
0.2425 

0.242s 

4.12S2 
4.1230 
4.1178 

0.9719 
0.9718 
0.9718 

23 
22 
21 
20 

19 

iS 

17 

o/2I<,3 

O.2247 

4.4494 

0-9757 

0.2363 

0.2432 

4.1126 

0.9717 

O.2I96 
O.2I98 
0.220I 

O.225I 
O.2254 
O.2257 

4-4434 
4-4373 
4-43^3 

0.9756 
0-9755 
0-9755 

0.2366 
0.2368 
0.2371 

0.2435 
0.2438 
0.2441 

4.1074 
4.1022 
4.0970 

0.9716 
0.9715 
0.9715 

44 
45 
46 

0.2204 
0.2207 
0.22IO 

0.2260 
O.2263 
0.2266 

4-4253 

4.4194 
4-4134 

0-9754 
0-9753 
0-9753 

16 
15 
14 

44 
45 
46 

0.2374 
0.2377 
0.2380 

0.2444 

0.2447 
0.2450 

4.0918 

4-0x17 
4.0815 

0.9714 

0.9713 
0.9713 

id 
15 
14 

47 

48 

49 

50 

51 

52 

53 

0.22I3 
0.22I5 

D.22  1  " 

O.2269 
0.2272 

O.2275 

4.4075 
4.4015 
4-3956 

o.9752 
0.9751 
<M,75i 

13 
12 

10 

9 

8 

7 

47 
48 

49 
50 

5i 

52 
53 

0.2383 
0.2385 

0.23S8 

0.2453 

O.2456 

0.2459 

4.0764 

4-0713 

4.o(>(>2 

0.9712 

0.0711 
0.0711 

13 
12 

10 

9 
8 

0.222I 

0.2278 

4-3«97 

0.9750 

0.2391 

0.2462 

4.01,1  1 

0.9710 

0.2224 
0.2227 
0.2230 

0.228  1 
O.2284 
O.2287 

4-3*38 
4-3779 
4-3721 

0.9750 

0-9749 
0.9748 

<>.23<M 
0.2397 
0.2399 

0.2465 
o.246g 

0.2472 

4.05(H) 
4.O509 

4-0459 

0.9709 
0.9709 
0.9708 

54 
55 
5'' 

0.2233 
0.2235 
0.2238 

O.229O 
O.2293 
O.2296 

4.3662 
4.3604 
4-3546 

0.9748 
0-9747 
0.9746 

6 

5 
4 

54 
55 
56 

0.2402 
0.2405 
0.2408 

0.2475 
0.2478 
0.2481 

4.0408 
4-0358 
4.0308 

0.9707 
0.9706 
0.9706 

6 

5 
4 

57 
58 
59 
BO 

0.224^ 
0.2244 
0.2247 

O.2299 

O.2303 

0.2  (0(1 

4-3488 
4-343Q 
4-3372 

0.9746 
0-9745 
0-9744 

3 
2 

1 
(» 

57 
58 
59 
60 

0.241 1 
0.2414 

0.2484 
0.2487 

0.2  |>|0 

4.0257 
4.0207 

4...15S 

0.9705 
0.9704 

0.071,4 

3 

1 
(1 

0.22:0   0.2309 

I-33IS 

0-9744 

0.24 1 9 

0.2493 

j.oioS 

0.9703 

Cos  |  ('«>( 

Tan 

Sin 

Cos 

Cot 

Tan 

Sin 

167' 


:il7 


/  / 


N  VIT 


<<> 


►166    -J.")!;0  *346° 


104°     194°  *284°       14° 


Natural 


15c 


115 
105°    195°  *285 


Sin 

Tan 

Cot 

Cos 

' 

Sin 

Tan 

Cot 

Cos 

0 

I 

2 

3 

0.2419 

0.2493 

4.0108 

0.9703 

60 

59 

53 
57 

0 

I 

3 

0.2588 

0.2591 
0.2594 
0.2597 

0-2679 
0.2683 

0.2686 
0.2689 

3-7321 
3-7277 
3-7234 
3-7I9I 

0.9657 

59 
5S 

57 

0.2422 
0.2425 
0.2428 

0.2496 
0.2499 
0.2503 

4.0058 
4.0009 
3-9959 

0.9702 
0.9702 
0.9701 

4 

5 
6 

0.2431 
0.2433 
0.2436 

0.2506 
0.2509 
0.2512 

3.9910 
3.9861 
3-9812 

0.9700 
0.9699 
0.9699 

56 

55 
54 

1 

s 

6 

0.2599 
0.2602 
0.2605 

0.2692 
0.2695 
0.2698 

3-7I43 
3-7I05" 
3.7062 

0.9655 

56 

55 
54 

7 

8 

9 

10 

ii 

12 

13 

c.2439 
0.2442 
0.2445 

0.2515 

0.2518 
0.2521 

3-9763 
3-97M 
3.9665 

0.9698 
0.9697 
0.9697 

53 
52 
5i 
50 

49 

48 
47 

7 

8 
9 
10 

1 1 
12 
t3 

0.2608 
0.261 1 
0.2613 

0.2701 
0.2704 
0.2708 

3-70I9 

3-''976 
3-6933 

0.9652 

53 
52 
5i 
50 

49 
43 
47 

0.2447 

0.2524 

3-96i7 

0.()ll(|(l 

(j.2()I() 

0.271 1 

3-6891 

<>.i,l>--2 

0.2450 
0.2453 
0.2456 

0.2527 
0.2530 
0.2533 

3-9568 
3-9520 
3-9471 

O.9695 
O.9694 
O.9694 

O.2619 
0.2622 
O.2625 

0.2714 
0.2717 
0.2720 

3.6848 
3.6806 
3.6764 

0.91.49 

14 

15 
16 

0.2459 
0.2462 
0.2464 

0.2537 
0.2540 
0.2543 

3-9423 
3-9375 
3.9327 

O.9693 
O.9692 
O.9692 

46 
45 
44 

14 

15 
16 

0.2628 
O.263O 
O.2633 

0.2723 
0.2726 
0.2729 

3.6722 
3.66S0 
3.6638 

0.9649 
0.964E 

0.9647 

46 
45 
44 

17 

18 

J9 

20 

21 

22 
23 

0.2467 
0.2470 
0.2473 

0.2546 

0.2549 
0.2552 

3-9279 
3.9232 
3.9184 

O.9691 
O.9690 
O.9689 

43 
42 
4i 
40 

39 
33 
37 

17 

18 

19 
20 

2r 
22 
2  3 

O.2636 
O.2639 
O.2642 

0.2733 
0.2736 
0.2739 

3-6596 

3-6554 

0.9646 
0.9646 
0.9645 

43 
42 
4i 
40 

39 
38 

0.2476 

0.2555 

3-9I36 

O.96S9 

O.2644 

0.2742 

3-6470 

0.2478 
0.2481 
0.2484 

0.2558 
0.2561 
0.2564 

3-9089 
3.9042 
3-8995 

O.9688 
O.9687 
O.9687 

O.2647 
O.265O 
O.2653 

0.2745 
0.2748 
0.2751 

3.6429 

3-6387 
3-6346 

0.9643 
0.9642 
0.9642 

24 

25 
26 

0.2487 
0.2490 
0.2493 

0.2568 
0.2571 
0.2574 

3-8947 
3.8900 

3-8854 

O.9686 
O.9685 
O.9684 

36 
35 
34 

24 

25 
26 

O.2656 
O.2658 
0.266I 

0.2754 
0.2758 
0.2761 

3-6305 
3.6264 
3.6222 

0.9641 

0.9640 

0.9639 

36 

35 
34 

27 
28 
29 

30 
3i 

32 

33 

0.2495 
0.2498 
0.2501 

0.2577 
0.2580 
0.2583 

3-8807 
3.8760 
3-87I4 

O.9684 
O.9683 
O.9682 

33 
32 
31 
30 

29 

28 

27 

27 
28 
29 
30 
31 
32 
33 

O.2664 
O.2667 
O.267O 

0.2764 
0.2767 
0.2770 

3.6181 
3-6140 
3.6100 

0.9639 
0.9638 
0.9637 

33 
32 
3i 
30 

29 

28 

0.2504 

0.2586 

3-86(,7 

O.9681 

0.2672 

0.2773 

3.6059 

1  ,.,,:,  ,1 

0.2507 
0.2509 
0.2512 

0.2589 
0.2592 
0.2595 

3.8621 

3-8575 
3-8528 

O.9681 
O.9680 
O.9679 

O.2675 
O.2678 
0.268I 

0.2776 
0.2780 
0.2783 

3.6018 
3-5978 
3-5937 

O.9636 
O.9635 
O.9634 

34 
35 
36 

0.2515 
0.2518 
0.2521 

0.2599 
0.2602 
0.2605 

3.8482 
3-8436 
3-839I 

O.9679 
O.9678 
O.9677 

26 
25 
24 

34 
35 
36 

O.2684 
0.2686 
O.2689 

0.2786 
0.2789 
0.2792 

3-5897 
3-5856 
3-5816 

O.9633 
O.9632 
O.9632 

26 
24 

37 
3S 
39 
40 

4i 
42 
43 

0.2524 
0.2526 
0.2529 

0.2608 
0.261 1 
0.2614 

3-8345 
3-8299 

3-8254 

O.9676 
O.9676 
O.9675 

23 
22 
21 
20 

19 

18 
17 

37 
38 
39 
40 

41 

42 
43 

O.2692 
O.2695 
O.2698 

0.2795 
0.279S 
0.2801 

3-5776 
3-5736 
3.5696 

O.963I 
O.963O 

".'/<>2<i 

23 

21 
20 

19 

18 
1 7 

0.2532 

0.2617 

3.8208 

O.9674 

O.27OO 

0.2S05 

3-5656 

(...,(,  2- 

0.2535 
0.2538 
0.2540 

0.2620 
0.2623 
0.2627 

3-8163 
3.8n8 
3-8073 

O.9673 
O.9673 
O.9672 

0.2703 
O.2706 
0.2709 

0.2808 
0.281 1 

0.2814 

3.5616 
3-5576 
3-5536 

O.9628 
O.9627 
O.9626 

44 
45 
46 

0.2543 
0.2546 
0.2549 

0.2630 
0.2633 
0.2636 

3.8028 
3-7983 
3-7938 

O.9671 
O.9670 
O.9670 

16 

15 
14 

44 
45 
46 

0.27I2 
O.27I4 
0.27I7 

0.2817 
0.2S20 
0.2823 

3-5497 
3-5457 
3-5418 

O.9625 
O.9625 
O.9624 

16 
14 

47 
48 
49 
50 

5i 

52 
53 

0.2552 
0.2554 
0.2557 

0.2639 
0.2642 
0.2645 

3-7893 
3-7848 
3-7804 

O.9669 
O.9668 
O.9667 

13 

11 
10 

9 

8 
7 

47 
48 
49 
50 

5i 
52 
53 

0.2720 
0.2723 
0.2726 

0.2827 
0.2830 
0.2833 

3-5379 
3-5339 
3-53oo 

O.9623 
O.9622 
O.962I 

1  ] 

10 

9 

8 

7 

0.2^.10 

0.2648 

3-776o 

O.9667 

0.2728 

0.2^3(1 

3.5261 

<>.')(>2I 

0.2563 
0.2566 
0.2569 

0.2651 
0.2655 
0.2658 

3-7715 
3-767I 
3-7627 

O.9666 
O.9665 
O.9665 

0.273I 
0.2734 
0.2737 

0.2839 
0.2842 
0.2845 

3.5222 

3-5I33 

3-5144 

O.962O 
O.96I9 

O.9618 

54 

55 
56 

0.2571 
0.2574 
0.2577 

0.2661 
0.2664 
0.2667 

3-7583 
3-7539 
3-7495 

O.9664 
O.9663 
O.9662 

6 

5 
4 

54 
55 
56 

0.2740 
O.2742 
0.2745 

0.2849 
0.2S52 
0.2S55 

3-5I05 
3-5o67 
3-5028 

O.9617 

6 

4 

57 
5S 
59 
60 

0.2580 
0.2583 
0.2585 

0.2670 
0.2673 
0.2676 

3-7451 
3.7408 
3-7364 

O.9662 
O.9661 
O.9660 

3 

2 

0 

57 
58 
59 
(50 

O.2748 
0.275I 
0.2754 

0.2858 
0.2861 
0.2864 

3-498g 

3-4951 
3.4  |I2 

O.9615 
O.9614 
O.9613 

3 
0 

0.2588 

0.2679 

3-7321 

O.9659 

0.275" 

0.2867  1  3.4874 

i).  |(>1  \ 

Cos 

Cot 

Tan  |  Sin 

Cos 

Cot  j  Tan 

Sin 

T65°  255°  *345° 


75° 


Natural 


ir,4°  254°  *344c 


116 
*106°     196 

0  *286° 

16° 

Natural 

17° 

*107° 

197°  *28 

70 

0 

i 

2 

3 

Sin     |    Tan 

( dt         Cos 

Sin        Tan 

Cot 

Cos 

0.2756  1  0.2867 

3-4874 

0.061 ; 

60 

59 

58 

0 

1 
2 
3 

0.2924 

0.3057 

0.9563 

60 

59 
58 

57 

0.2759 
0.2762 
0.2765 

0.2871 
0.2S74 
0.2877 

34836 

34798 
3.4760 

1  i.ol>I2 
O.96I  I 
O.96IO 

u.2o2<) 
O.2929 
O.2932 

0.3060 
0.3064 
0.3067 

3-2675 
3.2641 
3.2607 

0.9562 
0.9561 
0.9560 

4 

5 
C 

0.2768 
0.2770 
0.2773 

0.2880 
0.2883 
0.2886 

3.4722 
34684 
3.4646 

O.9609 
O.9609 
O.9608 

56 

55 
54 

4 
5 
6 

0.2935 
O.2938 
O.294O 

0.3070 
0.3073 
0.3076 

3-2573 
3-2539 
3.2506 

0.9560 
0.9559 
0.9558 

56 

55 
54 

7 
8 

9 
10 

II 

12 

c.2776 

0.2779 
0.2782 

0.2890 
0.2893 
0.2896 

3.4608 
34570 
34533 

O.9607 
O.9606 
O.9605 

53 
52 
51 
50 

49 
48 
47 

8 
9 
10 

13 

0.2943 
O.2946 
O.2949 

0.3080 
0.3083 
0.3086 

3-2472 
3-2438 
3-2405 

o.9557 
0.9556 
0.9555 

53 
52 
5i 
50 

49 

48 
47 

"•27.N 

0.2899 

34495 

O.9605 

O.2952 

0.3089 

3.2371 

o.9555 

0.2787 
0.2790 
0.2793 

0.2902 
0.2905 
0.2908 

34458 
3.4420 
34383 

O.9604 
O.9603 
O.9602 

O.2954 
0.2957 
O.2960 

0.3092 
0.3096 
0.3099 

3-2338 
3-2305 
3.2272 

o.9554 
o.9553 
0.9552 

14 
15 
16 

0.2795 
0.2798 
0.2801 

0.2912 
0.2915 
0.291S 

34340 
343oS 
34271 

O.960I 
O.960O 
O.96CO 

46 

45 
44 

14 
15 
16 

O.2963 
O.2965 
O.2968 

0.3102 
0.3105 
0.3108 

3.2238 
3.2205 
3.2172 

0.9551 
0.9550 
0.9549 

46 

45 
44 

17 
iS 

*9 

20 
21 
22 
23 

0.2804 
0.2807 
0.2809 

0.2921 
0.2924 
0.2927 

34^34 
34197 
3.4160 

0.9599 
O.9598 

0.9597 

43 
42 
41 
40 

39 
38 

37 

18 
19 
20 

21 
22 
23 

O.297I 
O.2974 
O.2977 

0.3m 
0.3115 
0.3118 

3-2139 
3.2106 
3-2073 

0.9548 
0.9548 
0.9547 

43 
42 
41 
40 

39 
38 

37 

0.2812 

0.2931 

34124 

O.9596 

O.2979 

0.3121 

3.2041 

0.9546 

0.2815 
0.2818 
0.2821 

0.2934 
0.2937 
0.2940 

3.4087 
34050 
3.4014 

O.9596 
0.9595 
0.9594 

O.2982 
O.2985 
O.2988 

0.3124 
0.3127 
0.3131 

3.2008 
3-1975 
3-1943 

0.9545 
0.9544 
0.9543 

24 

25 
26 

0.2823 
0.2826 
0.2829 

0.2943 
0.2946 
0.2949 

3-3977 
3-3941 
3-3904 

0.9593 
0.9592 
O.959I 

36 

35 
34 

24 

25 
26 

O.299O 
O.2993 
O.2996 

0.3134 
0.3137 
0.3140 

3-igio 

3.1878 
3-1845 

0.9542 
0.9542 

0.9541 

36 

35 
34 

27 

28 
29 

30 
31 
32 
33 

0.2832 

0.2835 
0.2S37 

0.2953 
0.2956 
0.2959 

3.3868 
3-3832 
3.3796 

O.959I 
O.959O 
O.9589 

33 
32 
3i 
30 

29 

28 

27 
28 
29 
30 
31 
32 
33 

O.2999 
O.3OO2 
O.30O4 

0.3143 
0.3147 
0.3150 

3-1813 
3.1780 
3-I748 

0.9540 
0-9539 

0.953S 

33 
32 
31 

30 

29 

28 
27 

O.2840 

0.2962 

3-3759 

0.95  88 

0.3007 

0.3153 

3-i7i6 

o.9537 

0.2843 
0.2S46 
0.2S49 

0.2965 
0.2968 

0.2972 

3-3723 
3.3687 
3-3652 

0.9587 
0.9587 
0.9586 

O.3OIO 
O.3OI3 
O.3OI5 

0.3156 
0.3159 
0.3163 

3.1684 

3.1652 
3.1620 

0.9536 
o.9535 
0-9535 

34 
35 
36 

0.2851 
0.2854 
0.2857 

0.2975 
0.2978 
0.2981 

3-36i6 
3-358o 

3-3544 

0.9585 
O.9584 
0.9583 

26 
25 
24 

34 
35 
36 

O.3O18 
O.302I 
0.3024 

0.3166 
0.3169 
0.3172 

3.1588 
3.I556 
3.I524 

o.9534 
0.9533 
0.9532 

26 
25 
24 

37 
38 
39 
40 

4i 
42 

43 

0.2860 
0.2862 
0.2865 

0.2984 
0.2987 
0.2991 

3-3509 
3-3473 
3-3438 

0.9582 
0.9582 
0.9581 

23 
22 
21 
20 

19 

18 

37 
38 
39 
40 

41 
42 
43 

O.3026 
O.3029 

n.illlJ 

0.3x75 
0.3179 
0.3182 

3.I492 
3.1460 

3.1420 

0.9531 
0.9530 
0.9529 

23 
22 

20 

19 
18 

0.2868 

•>.2uu4 

3-3402 

0.9580 

O.303J 

0.3185 

3-1397 

0.9528 

0.2-71 
0.2874 
0.2876 

O.2997 
0.3OO0 

O.3OO3 

3-3367 
3-3332 
3-3297 

0.9579 
0.9578 
0.9577 

O.3O38 
0.3040 
0.3043 

0.3188 
0.3191 
0.3195 

3.1366 
3-1334 
3-I303 

0.9527 
0.9527 
0.9526 

44 
45 
46 

0.2879 
0.2882 
0.2885 

O.3OO6 
O.3OIO 
O.3OI3 

3.3261 
3.3226 
3-3I9I 

0.9577 
0.9576 
0.9575 

16 

14 

44 
45 
46 

O.3O46 
0.3049 
0.305I 

0.3198 
0.3201 
0.3204 

3.127] 

3.1240 
3.1209 

0.9525 
0.9524 

0.9523 

15 
m 

47 
48 
49 
50 

5i 

52 
53 

0.2888 
O.2890 
O.2893 

O.3OI6 
O.3OI9 

(i.  5022 

3-3I56 
3.3122 
3-3087 

"■"574 
o.9573 
0.9572 

13 

12 
11 
10 

9 

8 
7 

47 

4s 

49 
50 
51 

52 

53 

0.3054 
0.3057 
O.3O6O 

0.3207 
0.321 1 
0.3214 

3-II78 
3. 1 146 
3-i"5 

0.9522 
0.9521 

0.9520 

12 

id 
9 

8 

o/ji-'o'' 

0.  ;>>-'<' 

3-3052 

0.9572 

0.3062 

0.3217 

;.io8  | 

0.9520 

"•-  ■'■•)•) 
0.2901 
O.2904 

1 1.3029 
O.3032 
0.3035 

3-30I7 
3-2983 
3.2948 

0.9571 
0.9570 
0.9569 

0.3065 
0.3068 
0.307I 

0.3220 
0.3223 
0.3227 

3-i<>53 
3.1022 
3.0991 

0.9519 

0.9518 
0.9517 

54 
55 
56 

0.2907 
0.2913 

O.3038 

O.3041 

3. 2,  ,14 
3-2879 
3-2845 

o.oV>~ 

0.9567 

0.9566 

6 

5 
4 

54 

55 
5<> 

0.3074 

O.3O76 
0.3079 

0.3230 
0.3233 
0.3236 

3.0961 
3.0930 

3.0899 

0.9516 
0.9515 

0.0514 

6 
5 

57 
58 
59 
80 

0.2918 
■  292] 

O.3048 
O.3051 
0.3054 

3.281 1 
3-2777 
3-2743 

0.9566 

0.9563 

0.9564 

3 

1 
(i 

5^ 
59 
80 

1  >.  ;o-j 
O.3085 
<>.  10K7 

0.3240 
0.3243 

0.  ^246 

3.0868 
3.0838 
3.0807 

0.9513 

0.9512 
0.951 1 

0 

, 

0.3057 

1.2709 

0.9563 

1 ,.  (i  191 1 

0  1249 

!.'>777 

0.0511 

Cob        Col 

Tan    |    Sin 

Cos     |     Cot          Tan          Sin 

163'  253' 


343' 


7:: 


N  \rn:  \i. 


1C»2° 


►108°  198°  *288° 


18° 


Natural 


19° 


117 

1011°  19«»c  *289° 


Tan 


Cot 


0.3090  I  0.3249 


0.3093 

0.309b  I 

0.3098 

0.3101 

0.3104 

0.3107 

0.31 10 

0.3112 

0.3115 


0.3118 


13 
14 
15 
16 

17 

18 

T9 
20 

21 
22 
23 
24 
25 
26 

27 
28 

29 
30 

31 

32 
33 
34 
35 
36 
37 
38 
39 
40 

4i 
42 
43 
44 
45 
46 

47 

48 

49 
50 

51 

52 
53 
54 
55 
56 

57 
58 
59 


0.3121 
0.3123 
0.3126 
0.3129 
0.3132 
0.3134 

o.3i37 
0.3140 
0.3M3 


o-3i45 


0.3148 
0.3151 
0.3I54 
0.3156 

03159 
0.3162 

0.3165 
0.3168 

0.3170 


0.3252 
0.3256 
0.3259 
0.3262 
0.3265 
0.3269 
0.3272 
0.3275 
0.3278 


0.3281 


0.3285 
0.3288 
0.3291 
0.3294 
0.3298 
0.3301 
0.3304 
0.3307 
Q-33IQ 


0.3314 


0.3176 

0.3179 
0.3181 

0.3184 
0.3187 
0.3190 
0.3192 
o.3i95 
0.3198 


0.3201 


0.3203 
0.3206 
0.3209 
0.3212 
0.3214 
0.3217 
0.3220 
0.3223 
0.3225 


o.33i7 
0.3320 
0.3323 

o.3327 
0.3330 
o.3333 
0.3336 
o.3339 
Q-3343 


3-Q777 


3-0746 
3.0716 
3.0686 

3.0655 
3.0625 
3-Q595 
3-0565 

3-0535 
3-0505 


3-0475 


3-0445 
3"^4T? 
3-0385 
3-0356 
3.0326 
3.0296 
3.0267 
3-Q237 
3.0208 


3.0178 


o.3346 


0-3349 
o.3352 
o.3356 

o.3359 
0.3362 

0.3365 
0.3369 
o.3372 
o.3375 


3.0149 
3.0120 
3.0090 
3.0061 
3.0032 
3.0003 
2-9974 
2-9945 
2.9916 


Cos 


0.95 1 1 


0.9510 
0.9509 
O.9508 

0.9507 
0.9506 
0.9505 
0.9504 
0.9503 

0.0502 


o.i|5<i'j 


0.9501 
0.9500 
0.9499 
0.9498 
0.9497 
0.9496 

0-9495 
0-9494 
0-9493 


0.9492 


2.98*7 


Q-3378 


0.3382 
0.3385 
0.3388 

o.339i 

o.3395 
o.3398 
0.3401 
0.3404 
0.3408 


0.3228 


0.3231 
0.3234 
0.3236 

0.3239 
0.3242 
0.324I 

0.3247 
0.3250 
0.3253 


0.3256 


Cos 


0.341 


0.3414 
0.3417 
0.3421 

0.3424 
0.3427 
0.3430 
0.3434 
0.3437 
0.3440 


Q-3443 


2.9858 
2.9829 
2.9800 
2.9772 
2-9743 
2.9714 

2.9686 
2.9657 
2.9629 


0.9492 
0.9491 

0.9490 

0.9489 
0.948S 
0.9487 
0.9486 
0.9485 
0-9484 


Q-94^3 


2.9600 


2.9572 
2-9544 
2.9515 
2.9487 
2-9459 
2.9431 
2.9403 
2-9375 
2-9347 


2-93 1 9 


2.9291 
2.9263 
2.9235 
2.9208 
2.9180 
2.9152 
2.9125 
2.9097 
2.9070 


0.9482 
0.9481 
0.9480 
0.9480 
o.9479 
0.9478 

o.9477 
0.9476 
o.9475 


o.9474 


o.9473 
0.9472 
0.9471 
0.9470 
0.9469 
0.9468 

0.9467 
0.9466 
0.9466 


0.9465 


0.9464 
0.9463 
0.9462 
0.9461 
0.9460 
0.9459 
0.9458 
0.9457 
0.9456 


Cot 


2.9042    ;    Q-945? 


Tan    I     Sin 


0 

Sin   Tan    Cot    Cos 

0.3256 

o.3443 

2.9042 

60 

59 
53 
57 

I 

3 

0.3258 
0.3261 

0.3264 

"•3447 
0.3450 
0-3453 

2.901  s 

2.8987 

2.8960 

0-9453 
0.9452 

4 
6 

0.3207 
0.3272 

o.3456 
0.3460 
0.3463 

2.8933 
2.8905 

2.8878 

0.9451 
0.9450 

0.9449 

56 
55 
54 

8 
9 

10 
1 1 
12 
13 

0.3275 
0.3278 
0.3280 

0.3466 
o.3473 

2.8851 

2.8824 
2-8797 

2.-77" 

0.9449 

0.9448 
Q-9447 
0.9446 

53 
52 
5i 
50 

49 
48 
47 

0.3283 

0.3476 

0.3286 
0.3289 
0.3291 

0-3479 
0.3482 
0.3486 

2.8743 
2.8716 
2.8689 

o.9445 

o.9444 
o.9443 

14 
15 
16 

0.3294 
0.3297 
0.3300 

0.3489 
0.3492 
0.3495 

2.8662 
2.8636 
2.8609 

0.9442 

0.9441 

0.9440 

46 
45 
44 

17 

18 

19 
20 
21 
22 

23 

0.3302 
0.3305 
0.3308 

0-3499 
0.3502 
0.3505 

2.8582 
2.8556 
2.8529 

o.9439 
0.9438 
0-9437 

43 
42 
4' 
40 

39 
38 

37 

0.331 1 

0.3508 

2.8502 

0.9436 

0.3313 
0.3316 

0.3319 

0.3512 
o.35i5 
0.3518 

2.8476 
2.8449 
2.8423 

0-9435 
0-9434 
0.9433 

24 

25 
26 

0.3322 
0.3324 
0.3327 

0.3522 
0.3525 
0.3528 

2.8397 
2.8370 
2.8344 

0.9432 

0.9431 
0.9430 

36 
35 
34 

27 

2S 
29 

30 

31 
32 
33 

0.3330 
o.3333 

o.3335 

0.353I 
0.3535 

o.3538 

2.8318 
2.8291 

2.8265 

0.9429 
0.9428 

0.9427 

33 
32 
3i 
80 

29 
2S 
27 

0.3338 

0.3541 

2.8239 

0.9426 

0.3341 
o.3344 
0.3346 

o.3544 
0.3548 
o.355i 

2.8213 
2.8187 
2.8161 

0.9425 
0.9424 
0.9423 

34 
35 
36 

o.3349 
0.3352 

o.3355 

0.3554 
o.3558 
0.3561 

2.8135 
2.8109 
2.8083 

0.9423 
0.9422 
0.9421 

26 
24 

37 
38 
39 
40 
41 
42 
43 

o.3357 
0.3360 
0.3363 

0.3564 
0.3567 
o.357i 

2.8057 
2.&032 
2.S006 

0.9420 
0.9419 
0.9418 

23 

21 
20 

10 
iS 
17 

0.3365 

0.3574 

2.7980 

0.9417 

0.330s 
0-337* 
0.3374 

o.3577 
0.3581 
0.3584 

2-7955 
2.7929 
2.7903 

0.9415 
0.9414 

44 
45 
46 

0.3376 
0.3379 
0.3382 

0.3587 
0.3590 
o.3594 

2.7878 
2.7S52 
2.7827 

0.9413 
0.9412 
0.94 1 1 

16 

15 
M 

47 
48 
49 
50 

51 
52 

53 

0.3385 
0.3387 
0.3390 

0.3597 
0.3600 
0.3604 

2.7801 

^.777" 
2.7751 

0.9410 
0.9408 

1 1 
10 

9 

o.3393 

O.3607 

2.7725 

0.9407 

0.3396 
o.3398 
0.3401 

0.3010 
0.3613 
0.3617 

2.7700 
2.767! 
2.7650 

0.9406 
0.9405 
0.9404 

54 
55 
56 

0.3404 
0.3407 
0.3409 

0.3620 
0.3623 
0.3627 

2.7625 
2.7600 
2-7575 

0.9403 
0.9402 
0.9401 

6 

5 
4 

57 
58 
59 
00 

0.3412 
0.34I5 
0.3417 

0.3630 
0.3633 
0.3636 

2.7550 
2.7525 
2.7500 

0.9400 
0.9399 
0.9398 

! 

0.3420 

0.3640 

2  7475 

'■<i3<>7 

0 

Cos    Cot   Tan 

Sin 

*161c  251°  *341c 


7r 


Natural 


,0 


T60°  250°  *340c 


118 
*110°  200c 


,O,)0c 


20c 


Natural 


2r 


411°  201°  *291° 


Sill  |  Tan  |  Cot  |  Cos  | 

0 

0.3420 

2.747s 

0.9397  60 

I 

2 
3 

0.3423 
0.3  128 

0.3643 
0.3646 
0.3650 

2.7450 
2.7425 
2.7400 

o.9395 
o.9394 

59 
58 

57 

4 
5 
(> 

0.3431 
o.3434 
o.3437 

0.3653 
0.3056 

0.3659 

2.7376 
2.7351 
2.7326 

0-9393 

0.9392 
0.9391 

56 
55 
54 

7 

S 

9 
10 

ii 

12 

13 

0-3439 

0.3442 
0.3445 
0.3448 

0.3663 
0.3666 

2.7302 

2.7277 

2-7  -  =  3 

0.9390 
0.9389 
0.9388 

52 
51 
50 

49 
48 
47 

0.3673 

2 .722  s 

0.9387 

0.3450 

o.3453 
0.3456 

O.3676 

0.3679 
0.3683 

2.7204 

2.7179 

2.7155 

0.9386 
0.9385 
0.9384 

i? 

10 

0.3458 
0.3461 

0.3464 

0.3686 
0.3689 
0.3693 

2.7130 
2.7106 
2.7082 

0.9383 
0.9382 
0.9381 

46 
45 
44 

17 
18 
1 9 
20 

21 
22 

23 

0.3467 
0.3469 
0.3472 

0.3696 
0.3699 
0.3702 

2.7058 
2.7034 
2.7009 

0.9380 

0.9379 
0.9378 

43 
42 
4i 
40 

39 

38 
37 

'■■3475 

0.3706 

2.6985 

o.9377 

0.3478 
0.3480 
0.3483 

0.3709 
0.3712 
0.3716 

2.6961 
2.6937 
2.6913 

0.9376 
o.9375 
o.9374 

24 

25 
26 

0.3486 
0.3488 
0.3491 

o.37i9 
0.3722 
0.3726 

2.6889 
2.6865 
2.6841 

o.9373 
0.9372 
0.9371 

36 
35 
34 

27 
28 
29 

30 

31 
32 

33 

0.3494 
o.3497 
0.3499 

0.3729 
0.3732 

o.3736 

2.6818 
2.6794 

2.6770 

0.9370 
0.9369 
0.9368 

33 

32 
3i 
30 

29 

28 
27 

0.3502 

o.3739 

2.6746 

0.9367 

0.3505 
0.3508 
0.3510 

o.3742 
o.3745 
o.3749 

2.6723 

2.6699 
2.6675 

0.9366 
0.9365 
0.9364 

34 
35 
36 

0.35I3 
0.3516 
0.3518 

o.3752 
o.3755 
0-3759 

2.6652 
2.6628 
2.6605 

0.9363 
0.9362 
0.9361 

26 
25 
24 

37 
38 
39 
40 

41 
42 

43 

0.3521 
o.3524 
o.3527 

0.3762 
o.3765 
0.3769 

2.6581 
2.6558 
2.6534 

0.9360 

0.9359 
0.9358 

23 
22 
21 
20 

19 

18 

17 

0.3529 

0.3772 

2.6511 

0.9356 

0.3532 
0.3535 
0.3537 

o.3775 
o.3779 
0.3782 

2.6488 

2.6464 
2.6441 

o.9355 
o.9354 
o.9353 

44 

45 
46 

0.3540 
o.3543 
o.3546 

0.3785 
0.3789 
0.3792 

2.6418 
2.6395 

2.6371 

0.9352 
0.9351 
0.9350 

10 
'5 
14 

47 
48 

49 
50 

5i 

52 
53 

o.3548 
o.355i 
o.3554 

0.3795 
o.3799 
0.3802 

2.6348 

2.6325 
2.6302 

0.9349 
0.9348 
o.9347 

13 
12 

in 

9 

S 

0.3557 

".  5*05 

2.6279 

0.9346 

0.3562 
0.3505 

i).  jSoy 
0.3812 
0.3815 

2.6256 
2.6233 
2.6210 

0.9345 

"■9344 
0-9343 

54 
55 
56 

0.3507 
0.3570 
0.3573 

0.3819 
0.3822 
0.3825 

2.6187 
2.0105 
2.6142 

0.9342 
O.934] 
O.9340 

5 
4 

57 
58 
59 
tin 

0.3576 

0.  J829 

0.3832 

2.6]  [9 

O.9339 
0.9338 
O.9337 

3 

2 
1 
0 

0   -  1 

0  339 

2.605] 

O.9336 

Cos  1  Cot  1  Tan  i   Sin 

Sin 

Tan  1  Cot    Cos 

0 

I 

2 

3 

o-3584 

0.3586 
0.3589 
0.3592 

0.3839  2.6051  0.9336 

60' 

59 
58 

57 

0.3845 
0.3849 

2.6028 

2.6006 
2.5983 

0-9335 

-,,334 
0-9333 

4 

5 
6 

0.3595 
o.3597 
0.3600 

0.3852 
0.3855 
0.3859 

2.51*01 
2.5938 
2.5916 

0.9332 
0.9331 
0.9330 

56 
55 
54 

8 
9 
10 
11 

J3 

0.3603 
0.3605 

(J.3O11S 

0.3862 
0.3865 
0.3869 

2.5893 

2.5-7' 
2.5-4- 

0.9328 
0.9327 
0.9326 

53 
52 
5i 
50 

49 

48 

47 

0.  ,Ol  I 

0.3872 

2.5-20 

0.9325 

0.3614 
0.3616 
0.3619 

0.3875 
0.3879 
0.3882 

2.5804 

2.5782 
2-5759 

O.9324 

0.9323 
0.9322 

14 
15 
16 

0.3622 
0.3624 
0.3627 

0.3885 
0.3889 
0.3892 

2-5737 
2.5715 
2.5693 

0.9321 
0.9320 
0.9319 

46 
45 

44 

17 

18 

19 
20 
21 
22 

23 

0.3630 
0.3633 
0.3635 

0.3895 
0.3899 
0.3902 

2.5671 
2.5649 

2.5627 

0.9318 
o.93i7 

1.93 10 

43 
42 
41 

m 

39 

3s 

37 

0.3638 

0.3906 

2.5605  |  0.9315 

0.3641 
0.3643 
0.3646 

0.3909 
0.3912 
0.3916 

=  ■5  5*3 
2.5561 

2-5539 

0-93M 
o.93i3 
0.9312 

24 
25 
26 

0.3649 
0.3651 
0.3654 

0.3919 
0.3922 
0.3926 

2.5517 
2-5495 
2-5473 

0.93 1 1 
0.9309 
0.9308 

36 

35 
34 

27 

28 

29 
30 

31 
32 
33 

0.3657 
0.3660 
0.3662 

0.3929 
0.3932 
0.3936 

2.5452 
2.5430 
2.540S 

0.9307 
0.9306 
0.9305 

33 
32 
31 
30 

29 

2S 

0.3665 

0.3939 

2.53S6  i  0.9304 

0.3668 
0.3670 
0.3673 

0.3942 
0.3946 
0.3949 

2.5365 
2-5343 
2.5322 

0.9303 
0.9302 
0.9301 

34 
35 

36 

0.3676 
0.3679 
0.3681 

o.3953 
0.3956 
o.3959 

2.5300 
2-5279 
2.5257 

0.9300 
0.9299 
0.9298 

20 
24 

37 
38 
39 
40 

41 
42 

43 
44 
45 
4<- 

0.3684 
0.3687 
0.3689 

.  0.3963 
0.3966 

0.  ;()t»i 

2.5236 
2.5214 
2.5193 

0.9297 
0.9296 
0.9295 

23 

20 

19 

iS 

1 7 
10 
15 
14 

0.3692 

o.3-)73 

2.5172 

O.9293 

0.369! 
0.3697 
0.3700 

0.3703 
0.3706 
0.3708 

0.3976 
C3979 
0.3983 
0.3986 
0.3990 
0-3993 

2.5150 
2.5120 
2.510S 
2.5086 
2.5065 
2.5044 

O.9292 

0.9291 
O.929O 

O.9288 

0.9287 

47 
48 
49 

50 

51 
52 
53 

0.371 1 
0.37U 
0.3716 

0.3996 
0.4000 
0.4003 

2.5023 
2.5002 
2.4981 

0.9286 
1 1.9285 
0.9284 

13 
12 
1 1 
10 

9 
8 

7 

o.37i9 

0.400O 

2.4960 

0.92S3 

0.3722 
0.3724 
o.3727 

0.4010 
O.4013 

0.4017 

2.4939 
2.4918 

2.4897 

O.9282 

0.9281 
O.9279 

54 
56 

0.3730 
"■3733 
0.3735 

0.4020 
O.4023 
O.4027 

2.4876 
2.485I 
2.4834 

■  1.9278 
O.9276 

(> 
5 
4 

57 
58 
50 

60 

0.3738 
o.374i 
Q-3743 
0.3746 

0.4030 
O.4033 

0.  (037 
O.4040 

2.4813 
2.4792 
2-4772 

2.4751 

...0275 
..,,274 
0.9273 

-.,,272 

3 

1 
11 

Cos    Cot    Tan  |  Sin 

»15fl    249 


69° 


N  \  11  1:  \i. 


68 


158    248      338 


►112°  202°  *292 


99° 


Natural 


23° 


119 
►113    203°  *293° 


Sin   Tan    Cot    Cos 

0 

0.3746 

0.4040 

2.4751 

0.9272 

60 

59 

o.3749 

O.4044 

2.4730 

0.1,271 

2 

0.3751 

0.4047 

2.4709 

0.9270 

58 

3 

"•3754 

0.4050 

2.46S9 

0.9269 

57 

4 

o.3757 

0.4054 

2.4668 

0.9267 

56 

5 

0.3760 

0.4057 

2.4648 

0.9266 

55 

6 

0.3762 

0.401a 

2.4627 

0.9265 

54 

7 

o.37£>5 

0.4064 

2.4606 

0.9264 

53 

8 

0.3768 

0.4067 

2.4586 

0.9263 

52 

9 
10 

ii 

0.3770 

0.4071 

2.4566 

0.9262 

51 
50 
49 

0-3773 

0.4074 

24545 

0.9261 

O.3770 

0.4078 

2.4525 

0.9260 

12 

0.3778 

0.4081 

2.4504 

0.9259 

48 

13 

0.3781 

0.40S4 

2.4484 

0.9258 

47 

14 

0.3784 

0.4088 

2.4464 

0.9257 

46 

IS 

0.3786 

0.4091 

2-4443 

0.9255 

45 

16 

0.3789 

0.4095 

2.4423 

0.9254 

44 

17 

0.3792 

0.4098 

2.4403 

0.9253 

43 

IS 

0-3795 

0.4101 

2.43S3 

0.9252 

42 

19 
20 

21 

0-3797 

0.4105 

2.4362 

0.9251 

4i 
40 
39 

0.3800 

0.4108 

2.4342 

0.9250 

0.3803 

0.41 1 1 

2.4322 

0.9249 

22 

0.3805 

0.41 1 5 

2.4302 

0.9248 

38 

23 

0.3808 

0.41 1 8 

2.4282 

0.9247 

37 

24 

0.3811 

0.4122 

2.4262 

0.9245 

36 

25 

0.3813 

0.4125 

2.4242 

0.9244 

35 

26 

0.3816 

0.4129 

2.4222 

0.9243 

34 

27 

0.3819 

0.4132 

2.4202 

0.9242 

33 

28 

0.3S21 

0.4x35 

2.4182 

0.9241 

32 

29 
30 

31 

0.3824 

0.4139 

2.4162 

0.9240 

3i 
30 
29 

0.3827 

0.4142 

2.4142 

0.9239 

0.3830 

0.4146 

2.4122 

0.9238 

32 

0.3S32 

0.4149 

2.4102 

0.9237 

2S 

33 

0.3835 

0.4152 

2.4083 

0.9235 

27 

34 

0.3S38 

0.4156 

2.4063 

0.9234 

26 

35 

0.3840 

0.4159 

2.4043 

0.9233 

25 

36 

0.3843 

0.4163 

2.4023 

0.9232 

24 

37 

0.3846 

0.4166 

2.4004 

0.9231 

23 

38 

0.3S48 

0.4169 

2.39S4 

0.9230 

22 

39 
40 

41 

0.3851 

0.4173 

2.3964 

0.9229 

21 

20 

19 

0.3854 

0.4176 

2-3945 

0.9228 

0.3856 

0.41  So 

2.3925 

0.9227 

42 

0.3859 

0.4183 

2.3906 

0.9225 

18 

43 

0.3862 

0.4107 

2.3886 

0.9224 

17 

44 

0.3S64 

0.4190 

2.3867 

0.9223 

16 

4? 

0.3867 

0.4193 

2.3847 

0.9222 

15 

46 

0.3870 

0.4197 

2.382S 

0.9221 

14 

47 

0.3872 

0.4200 

2.3808 

0.9220 

13 

48 

0.3875 

0.4204 

2.3789 

0.9219 

12 

49 
50 

5i 

0.3878 

0.4207 

2.3770 

0.9218 

10 

9 

0.3881 

0.4210 

2.3750 

0.9216 

0.3883 

0.4214 

2.3731 

0.9215 

52 

0.3SS6 

0.4217 

2.3712 

0.9214 

8 

53 

0.3889 

0.4221 

2.3693 

0.9213 

7 

54 

0.3S91 

0.4224 

2.3673 

0.9212 

6 

55 

0.3S94 

0.4228 

2.3654 

0.92 1 1 

3 

56 

0.3897 

0.4231 

2.3635 

0.9210 

4 

57 

0.3899 

0.4234 

2.3616 

0.9208 

3 

58 

0.3902 

0.42  3  S 

2-3597 

0.9207 

2 

59 
60 

0.3905 

0.4241 

2.3578 

0.9206 

1 

0.3907 

0.424! 

2-3559  1  0.9205 

0 

|  Cos 

Cot 

Tan    Sin 

' 

SiD    T;m 

Col   Cos 

0 

1 
3 

0.3907 

0-4245 

2.3559 

0.9205 

60 

59 

58 
57 

0.  ;i,in 
0.39I5 

0.4252 
0.4255 

2.3=  (9 
2.3520 
2.350I 

0.9204 
0.9203 
0.9202 

4 

5 
6 

O.3918 
O.392I 
0.3923 

0.4262 

0.4265 

2.3483 
2.3464 
2-3445 

0.9200 
0.9198 

56 
55 
54 

7 
8 
9 
10 

12 

13 

O.3926 
O.3929 

0.3031 

0.4269 

0.4272 
0.  !-•;' 

2.3426 
2.3388 

0.9196 
0.9195" 

53 
52 
5i 
50 

49 

r 
47 

0.3934 

0.4279 

2.3369 

0.9194 

o.3937 
0-3939 
0.3942 

0.4283 
0.4286 
0.42S9 

2.3351 

2.3332 
2-3313 

0.9192 

14 

15 
16 

0.3945 
o.3947 
0.3950 

0.4293 
0.4296 
0.4300 

2.3294 
2.3276 
2.3257 

0.9189 
0.9188 
0.9187 

46 
45 
44 

17 
18 
19 
20 
21 
22 
23 

o.3953 
o.3955 
0.3958 

0.4303 
0.4307 
0.4310 

2.3238 
2.3220 
2.3201 

0.9186 
0.9184 

0.9 1  -3 

43 
42 
41 
40 

39 

33 
37 

0.3961 

0.4314 

2.31  -3 

o..,I  .-2 

0.3963 
0.3966 
0.3969 

0.4317 
0.4320 
0.4324 

2.3164 
2.3146 

2.3127 

0.9101 
0.9180 

0.9179 

24 
25 
•26 

0.3971 
o.3974 
o.3977 

0.4327 
0.4331 
o.4334 

2.3109 
2.3090 
2.3072 

0.9178 
0.9176 
0.9175 

36 
35 
34 

27 
28 
29 
30 

31 
32 
33 
34 
35 
36 

o.3979 

0.39S2 
0.3985 

0.4338 
0.4341 
o.4345 

2.3053 
2.3035 
2.3017 

0.9174 
0.9173 

0.9172 

33 
32 
3i 
30 
29 
28 
27 
26 
25 
24 

0.39S7 

0.4348 

2.299S 

0.91 71 

0.3990 
o.3993 
0-3995 
0.3998 
0.4001 
0.4003 

0.4352 
0.4355 
0.4359 
0.4362 
0.4365 
0.4369 

2.2980 
2.2962 
2.2944 
2.2925 
2.2907 
2.2889 

0.9169 

0.9168 
0.9167 

0.9166 
0.9165 
0.9164 

37 
38 
39 
40 

41 
42 
43 

0.4006 
0.4009 
0.401 1 

0.4372 
0.4376 
0.4379 

2.2871 

2.2S53 
2.2  \;; 

0.9162 
0.9161 

0.1,160 

23 

20 

19 

18 

17 

0.4014 

0.4383 

2.2817 

o.,,,?i, 

0.4017 
0.4019 
0.4022 

0.4386 
0.4390 
o.4393 

2.2709 
2.2763 

0.9158 
0.9157 
0.9155 

44 
45 
46 

0.4025 
0.4027 
0.4030 

0.4397 
0.4400 
0.4404 

2.2745 
2.2727 
2.2709 

0.9154 
0.9152 

16 
x5 
14 

47 

4s 

49 
50 

5i 
52 
53 

0.4033 

0.4035 
0.4038 

0.4407 
0.4411 
0.4414 

2.2691 
2.2673 
2.2655 

0.9151 
0.9150 

0.914s 

13 

12 
1  1 
10 

9 

8 

0.4041 

0.4417 

2.2637 

0.9147 

0.4043 
0.4046 
0.4049 

0.4421 
0.4424 
0.442S 

2.2620 

2.2602 
2.2584 

0.9146 
0.9145 
0.9144 

54 

55 
56 

0.4051 
0.4054 
0.4057 

0.4431 

"•443? 
0.4438 

2.2566 
2-2549 
2.2531 

0.9143 

0.9141 

0.9140 

b 

5 
4 

57 
58 
59 
60 

0.4059 
0.4062 
0.4065 

O.4442 

"•4445 
0.4449 

2.2513  0.9139 

2.2496  |  0.9138 

0.9137 

3 

2 

1  1 

0 

0.4067  |  0.4452 

_._■  j(,n   0.1,13; 

Cos  |  Cot 

Tan  |  Sin 

157°  247°  *337 


67* 


Natural 


00° 


456°  240°  *33(5U 


i20 

*114°  204°  *-2UV 


24c 


Natural 


25°       *115°  205°  *295c 


Si i)     |    Tan 

Cot 

Cos 

(1 

2 

3 

04067  |  0.4452 

2.2460 

-•.2443 
2.2425 
2.2408 

0.9135 

till 

59 

58 
57 

"■4"7' ' 
O.4073 
O.4075 

0.4456 

0.4459 
0.4463 

0.9134 
0.9133 
0.9132 

■( 
5 
6 

04078 

0.4081 
O.4083 

0.4466 
0.4470 

".4473 

2.2390 
2.2373 
2.2355 

0.9131 
0.9130 
0.9128 

56 
55 
54 

3 
9 
10 
I] 

12 

13 

0.4086 
0.4089 

0.4091 

0.4477 
0.4480 
0.4484 

2.2338 
2.2320 
2.2303 

0.9127 
0.9126 
0.9125 

53 
51 

50 

49 
48 

47 

0.4004 

0.44*7 

2.2286 

0.9124 

0.4097 
0.4099 
0.4102 

04491 
0.4494 
04498 

2.2268 
2.2251 
2.2234 

0.9122 
0.9121 
0.9120 

15 
16 

0.4105 
0.4107 
0.4110 

0.4501 
04505 
0.4508 

2.2216 
2.2199 
2.2182 

0.9119 
0.9118 
0.9116 

46 

45 
44 

'7 
18 

19 

20 
21 
22 

23 

0.41 12 

0.41 1  5 
0.4118 

0.4512 
04515 
04519 

2.2165 
2.2148 
2.2130 

0.91 1 5 
0.91 14 
0.91 13 

43 
42 
4i 
40 

39 
38 
37 

0.4120 

0.4522 

2.2113 

0.91 12 

0.4123 
0.4126 
0.4128 

0.4526 
0.4529 
04533 

2.2096 
2.2079 
2.2062 

0.91 10 
0.9109 
0.9108 

24 

25 
26 

0.4131 
04134 
0.4136 

04536 
0.4540 
04543 

2.2045 
2.2028 
2.2011 

0.9107 
0.9106 
0.9104 

36 

35 
34 

27 

28 

29 
30 

3i 
32 

33 

04139 
0.4142 

0.4144 

04547 
0.4550 
04554 

2.1994 

2.1977 
2.1960 

0.9103 
0.9102 
0.9101 

33 
32 
31 
30 
29 
28 

0.4147   1  , 

2.1943 

0.9100 

0.4150 
0.4152 
0.4I55 

04561 
04564 
04568 

2.1926 
2.1909 
2.1892 

0.9098 
0.9097 
0.9096 

34 
35 
36 

0.4158 
0.4160 
O.4163 

04571 
04575 
04578 

2.1876 
2.1859 
2.1842 

0.9095 
0.9094 
0.9092 

26 
25 
24 

37 
33 
39 
40 

41 
42 

43 

0.4165 
0.4168 
0.41 71 

0.4582 
04585 
04589 

2.1825 
2.1808 
2.1792 

0.909 1 
0.9090 

0.9089 

23 

20 

19 

18 
17 

0.4I73 

04592 

2-1775 

0.90S8 

0.4176 
0.4179 
0.4181 

0.4596 
04599 
0.4603 

2.1758 
2.1742 
2.1725 

0.9086 
0.9085 
0.9084 

44 
45 
46 

O.4184 

0.4187 
0.4189 

0.4607 
0.4610 

0.  (Ol) 

2.1708 
2.1692 
2.1675 

0.9083 
0.9081 
0.9080 

16 

'5 
14 

47 

4s 
49 
50 

5i 
52 
53 

O.4192 
O.4195 

'MI97 

0.4617 
0.4621 

0.  (62 ) 

2.1659 
2.1642 

2.  102-. 

0.9079 

0.907s 
0.9077 

13 
12 

10 

9 

8 
7 

O.  |2oi  1 

0.4628 

2.1609 

0.9075 

0.4202 
0.4205 
0.4208 

0.4631 

0.4635 
0.4638 

2.1592 
2.1576 
2.1560 

0.9074 
0.9073 
0.9072 

54 
55 
56 

0   |.2I0 
O.4213 
O.42X6 

0.4642 

0.4645 

0.4(1 19 

2-1543 
2.1527 
2.1510 

0.9070 

0.9.  .in, 

6 

5 
4 

57 
58 
59 
60 

O.4218 
0.  |'-'-'i 
O.4224 

0.4652 
0.4656 
0.4660 

2.1494 

2.1478 
2.1461 

O.9O67 
O.9O66 

1   I.9I   ,(  4 

3 

1 
0 

0.4226 

0,  |Od;   j   2.1445   |  0.9063 

Cos        Cot    |   Tan        sin 

' 

Bin 

Tan 

|    Cot 

1    Cos 

0 

1 

0.4226 

0.4663 

2.1445 

0.9063 

60 

0.4229 

04667 

2.1429 

0.9062 

59 

2 

04231 

0.4670 

2.1413 

0.9061 

sS 

3 

04234 

04674 

2.1396 

0.9059 

57 

4 

0.4237 

0.4677 

2.1380 

0.9058 

56 

5 

04239 

0.4681 

2.1364 

0.9057 

55 

6 

0.4242 

04684 

2.1348 

0.9056 

54 

7 

04245 

04688 

•2.1332 

0.9054 

53 

8 

04247 

04691 

2.1315 

0.9053 

S2 

9 
10 

11 

04250 

0.4695 

2.1299 

0.9052 

51 

50 

40 

04253 

04699 

2.1283 

0.9051 

04255 

04702 

2.1267 

0.9050 

12 

04258 

04706 

2.1251 

0.9048 

43 

13 

0.4260 

0.4709 

2.1235 

0.9047 

47 

M 

04263 

04713 

2.1219 

0.9046 

46 

15 

04266 

0.4716 

2.1203 

0.9045 

45 

16 

04268 

0.4720 

2.1187 

0.9043 

44 

I7 

0.4271 

04723 

2.1171 

0.9042 

43 

lb 

0.4274 

0.4727 

2.1155 

0.9041 

42 

19 

20 

21 

04276 

04731 

2.1139 

0.9040 

4i 
40 

39 

0.4279 

04734 

2.1123 

0.9038 

0.4281 

0.4738 

2.1107 

0.9037 

22 

04284 

04741 

2.1092 

0.9036 

38 

23 

0.4287 

04745 

2.1076 

0.9035 

37 

24 

04289 

0.4748 

2.1060 

0.9033 

36 

25 

0.4292 

04752 

2.1044 

0.9032 

35 

26 

0.4295 

04755 

2.1028 

0.9031 

34 

27 

0.4297 

0.4759 

2.1013 

0.9030 

33 

28 

0.4300 

04763 

2.0997 

0.9028 

32 

29 

30 
31 

04302 

04766 

2.0981 

0.9027 

31 
30 
29 

0.4305 

0.4770 

2.0965 

0.9026 

0.430S 

04773 

2.0950 

0.9025 

32 

0.4310 

04777 

2.0934 

0.9023 

23 

33 

04313 

047S0 

2.0918 

0.9022 

27 

34 
35 
16 

0.4316 

04784 

2.0903 

0.9021 

26 

04318 

0.4788 

2.0887 

0.9020 

25 

04321 

0.4791 

2.0872 

0.9018 

24 

37 
33 
39 
40 

4i 
42 
43 
44 
45 
46 

04323 

04795 

2.0856 

0.9017 

23 

04326 

0.4798 

2.0840 

0.9016 

22 

0.4329 

04802 

2.0S25 

0.9015 

21 
20 
J9 

0.4331 

o.4S(,(, 

2.0809 

0.901  -, 

0.4334 

0.4S09 

2.0794 

« 1.91  >]  2 

04337 

0.4SI3 

2.077S 

0.901 1 

iS 

04339 

0.4816 

2.0763 

0.9010 

17 

0.4342 

0.4820 

2.0748 

0.9008 

11. 

0.4344 

0.4823 

2.0732 

0.9007 

15 

04347 

0.4827 

2.0717 

0.9006 

'4 

47 
48 
49 
50 

04350 

0.4831 

2.0701 

0.9004 

13 

04352 

0.4834 

2.0686 

0.9003 

12 

04355 

0.4S3S 

2.0(171 

0.91  >i  >2 

1  I 
10 
9 

04358 

0.4841 

2.o(>55 

...90,9 

0.4360 

0.4S45 

2.0(140 

o.S,,99 

52 
53 
54 
55 
56 
57 

04363 

0.4S49 

2.0625 

0.S998 

8 

0.4365 

0.4852 

2.0609 

O.8997 

7 

04368 

0.4856 

2.0594 

<  1.S99O 

6 

04371 

04S59 

2-0579 

O.8994 

5 

04373 

0.4863 

2.0564 

O.8993 

4 

0. 1 176 

0.4867 

2.054.) 

O.8992 

3 

0.4378 

0.4870  1 

2-0533 

O.899O 

2 

58 

0.43  s, 

04874    ! 

2.051s 

0.81)89 

1 
0 

59 

60 

04384 

o.4*77    | 

2.0503 

O.898S 

('os    1    Cot    ! 

Tan 

Sin 

65 


N  V.TUB  \l. 


C»l 


154  '  244°  *334° 


416°  206°  *296° 


26c 


Natural 


27 


121 
117°  207°  *297° 


' 

Sin  j  Tan  1  Cot 

Cos 

0 

I 

0.4384 

0.4877 

2.0503 

<  !.><>>> 

60 

59 

0.4386 

0.4SS1 

2.0488 

.>.>.,.- 7 

2 

0.4389 

0.4885 

2.0473 

O.8985 

58 

3 

0.4392 

0.4888 

2.0458 

0.8984 

57 

4 

0.4394 

0.4892 

2.0443 

O.8983 

56 

S 

o.4397 

0.4895 

2.0428 

O.8982 

55 

6 

o.4399 

0.4899 

2.0413 

,,.>,,-,, 

54 

7 

0.4402 

0.4903 

2.0398 

0.8979 

53 

8 

0.4405 

0.4906 

2.0383 

O.8978 

52 

9 
10 

n 

0.4407 

0.4910 

2.0368 

0.8976 

51 
50 
49 

0.4410 

0.4913 

2.0353 

0.8975 

0.4412 

0.4917 

2.0338 

O.S974 

12 

0.4415 

0.4921 

2.0323 

0.8973 

48 

13 

0.44 1 8 

0.4924 

,-2.0308 

O.8971 

47 

14 

0.4420 

0.4928 

2.0293 

0.8970 

46 

15 

0.4423 

0.4931 

2.0278 

0.8969 

45 

16 

0.4425 

0.4935 

2.0263 

0.8967 

44 

17 

0.442S 

0.4939 

2.0248 

0.8966 

43 

18 

0.4431 

0.4942 

2.0233 

0.8965 

42 

J9 
20 

21 

0.4433 

0.4946 

2.0219 

0.8964 

4i 
40 

39 

0.4436 

0.49I0 

2.0204 

0.8962 

0.4439 

0-4953 

2.0189 

0.8961 

22 

0.4441 

0-4957 

2.0174 

0.8960 

38 

23 

0.4444 

0.4960 

2.0160 

0.8958 

37 

24 

0.4446 

0.4964 

2.0145 

O.8957 

36 

25 

0.4449 

0.4968 

2.0130 

0.8956 

35 

26 

0.4452 

0.4971 

2.01 1 5 

0.8955 

34 

27 

o.4454 

0.4975 

2.0101 

O.8953 

33 

23 

0.445  7 

0.4979 

2.0086 

O.8952 

32 

29 

30 

3i 

0.4459 

0.4982 

2.0072 

0.8951 

3i 
30 
29 

0.4462 

0.49S6 

2.0057 

0.-0.40 

O.446! 

0.49S9 

2.0042 

0.8948 

32 

0.4467 

0.4993 

2.0028 

0.8947 

28 

33 

0.4470 

0.4997 

2.0013 

0.8945 

27 

34 

0.4472 

0.5000 

1.9999 

0.8944 

26 

35 

0-4475 

0.5004 

1.99S4 

O.8943 

25 

36 

0.4478 

0.5008 

1.9970 

O.S942 

24 

37 

0.44S0 

0.5011 

1-9955 

0.8940 

23 

33 

0.4483 

0.5015 

1. 994 1 

O.8939 

22 

39 
40 

4i 

0.4485 

0.5019 

1.9926 

0.S93S 

20 

19 

0.4488 

0.5022 

1.9912 

0.8936- 

0.4491 

0.5026 

1.9897 

0.8935 

42 

o.4493 

0.5029 

1.9883 

0.8934 

18 

43 

0.4496 

0.5033 

1.9868 

0.8932 

17 

44 

0.4498 

0.5037 

1.9854 

0.8931 

16 

4^ 

0.4501 

0.5040 

1.9840 

0.8930 

15 

46 

0.4504 

0.5044 

1.9825 

0.8928 

14 

47 

0.4506 

0.5048 

1.9811 

0.S927 

13 

4s 

0.4509 

0.5051 

1-9797 

0.8926 

12 

49 
50 

Si 

0.451 1 

0.5055 

1.9782 

0.8925 

10 

9 

0.4514 

0.505., 

1.9768 

0.8923 

0.45I7 

0.5062 

1-9754 

0.8922 

52 

0.4519 

0.5066 

1.9740 

0.8921 

8 

53 

0.4522 

0.5070 

1.9725 

0.8919 

7 

54 

0.4524 

0.5073 

1.9711 

0.8918 

6 

55 

0.4527 

0.5077 

1.9697 

0.8917 

5 

56 

0.4530 

0.5081 

1.9683 

0.8915 

4 

57 

o.4532 

0.5084 

1.9669 

0.8914 

3 

58 

0.4535 

0.5088 

I-9654 

0.8913 

2 

59 
60 

0.4537 

O.50.J2 

1.9640 

0.8911 

0 

0.4540 

0.1:005 

1.9626 

0.8910 

Cos  J  Cot  |  Tan  \     Sin 

sin  j  Tan 

Cot  |  Cos 

0 

1 

0.4540 

0.5095 

[.9626 

0.8910 

60 

59 

0.4542 

0.5099 

1. 96 1  2 

0.8909 

2 

0.4545 

0.5103 

1.9598 

0.8907 

58 

3 

0.4548 

0.5106 

19584 

0.8906 

57 

4 

0.4550 

0.5110 

1.9570 

0.8905 

56 

5 

0.4553 

0.5114 

1 9556 

0.8903 

55 

6 

0.4555 

0.5II7 

0.8902 

54 

7 

0.4558 

0.5121 

19528 

0.8901 

53 

8 

0.4561 

0.5125 

1.9514 

0.8899 

52 

9 
10 

0.4563 

0.5128 

[.9500 

0.8898 

51 
B0 
49 

0.4566 

0.5132 

1.9486 

0.8897 

0.450.- 

0.5136 

1.9472 

12 

0.4571  0.5139 

1.9458 

0.8894 

4« 

13 

0.4574  0.5143 

1.9444 

0.8893 

47 

14 

0.4576 

0.5147 

1.9430 

0.8892 

4'' 

15 

0.4579 

0.5150 

1.9416 

0.8890 

45 

16 

0.4581 

o.5i54 

1.9402 

0.8889 

44 

17 

0.4584 

0.5158 

1.9388 

0.8888 

43 

18 

0.4586 

0.5161 

1-9375 

0.8886 

42 

19 
20 
21 

0.4589 

0.5165 

1.9361 

0.8885 

4i 
10 
39 

0.4592 

0.5169 

1-9347 

0.8884 

0.4594 

0.5172 

1-9333 

22 

0.4597 

0.5176 

I.93I9 

0.8881 

38 

23 

0.4599 

0.5180 

1.9306 

0.8879 

37 

24 

0.4602 

0.5184 

1.9292 

0.8878 

36 

25 

0.460? 

0.5187 

1.9278 

0.8877 

35 

26 

0.4607 

0.5191 

1.9265 

0.8875 

34 

27 

0.4610 

0.5195 

1-9251 

0.8  S  74 

33 

28 

0.4612 

0.5198 

[.9237 

0.8873 

32 

29 
30 
31 

0.4615 

0.5202 

1.9223 

0.8871 

3i 
30 
29 

0.4617 

0. 5  206 

1. 92 10  |  .: 

0.4620 

0.5209 

1.9x96 

0.8869 

32 

0.4623 

0.5213 

1.9183 

0.8867 

28 

33 

0.4625 

0.5217 

1.9x69 

0.8866 

27 

^4 

0.4628 

0.5220 

I-9I55 

0.8865 

26 

35 

0.4630 

0.5224 

1.9142 

0.8863 

25 

.36 

0.4633 

0.5228 

1.9x28 

0.8862 

24 

37 

0.4636 

0.5232 

1.9115 

0.8861 

23 

38 

0.4638 

0.5235 

1.9101 

0.8859 

22 

39 

40 

41 

0.4641 

0.5239 

[.9088 

0.8858 

21 
20 

19 

0.4643 

0.5243 

i-9'-'74 

0.8857 

o->>55 

0.4646 

0.5246 

1.90(11 

42 

0.4648 

0.5250 

I.9047 

0.8S54 

18 

43 

0.4651 

0.5254 

I.9034 

0.8853 

17 

44 

0.4654 

0.5258 

I.9020 

0.8851 

16 

45 

0.4656 

0.5261 

I.9007 

O.8S50 

J5 

46 

0.4659 

0.5265 

I.8993 

14 

47 

0.4661 

0.5269 

I.8980 

0.S847 

13 

48 

0.4664 

0.5272 

O.8S46 

12 

49 
50 
51 

0.4666 

0.5276 

1.8953 

0.8844 

11 
10 
9 

,  1.40.11, 

0.5280 

l.-o|" 

o.>.-43 

0.4672 

0.^2-4 

I.S927 

0.8842 

52 

0.4674 

0,5287 

1. 8913 

0.8840 

s 

53 

0.4677 

0.5291 

1.8900 

0.S839 

7 

54 

0.4679 

0.529! 

1.8887 

0.8838 

6 

55 

0.4682 

O.5298 

1.8873 

5 

56 

0.4684 

0.5302 

1.8860 

0.8835 

4 

57 

0.4687 

0.5306 

1.8847 

0.8834 

3 

58 

0.4690 

0.5310 

1.8834 

O.8832 

2 

59 
60 

0.4692 

o.53i3 

1.8820 

0.8831 

0 

0.4695 

0.5317 

1.8807 

0.8829 

Cos  1  Cot 

,  Tan  |  Sin 

153°  243°  *333°       03° 


Natural 


02°       »152°  242°  *332 


122 

I  is    -Jus0  *298° 


28c 


Natural 


29c 


119°  209°  *299° 


Sin 

Tail 

Cot 

Cos 

0 

1 

3 

0.4693 

0.5317 

1.SS07 

.8829 

60 

59 

58 

57 

"■47"-' 

0.5321 

0.5325 
0.5328 

1.8794 
[.878] 

1.8768 

0.8827 
0.8825 

4 
5 
6 

o.5332 
o.5336 
0.5340 

c.8755 
[.8741 

1.8728 

0.8824 
0.8823 
0.8821 

50 
55 
54 

8 
9 
10 

II 

12 

13 

"•4713 
0.4715 
O.4718 

0-5343 
o.5347 
o.535i 

1.8715 
1.8702 

I.SI.S,, 

0.8820 
0.8819 

0.SS17 

53 
52 
5i 
50 

49 
48 
47 

0.4720 

o.5354 

I.S(.7(. 

d.SMI, 

0-4723 
0.4726 
O.4728 

<>-535^ 
0.5362 
0.5366 

I.SM.3 
1.8650 

1.8637 

O.8814 

O.8813 
0.88I2 

16 

0.473I 
o.4733 

"■473'' 

0.5369 
o.5373 
0.5377 

I.S624 
1.8611 
I.S598 

0.88IO 
O.8S09 
O.8808 

46 
45 
44 

iS 
19 
20 
21 
22 
23 

0.4738 

0.4741 
0.4743 

0.5381 
0.5384 
0.5388 

1.8585 
1.8572 
1-8559 

O.8806 
O.8805 
O.8803 

43 
42 
4i 
40 

39 

38 
37 

0.4746 

o.5392 

1.8546 

O.8802 

0.4749 

"■47?  1 
0.4754 

0.5  39° 
o.5399 
0.5403 

1-8533 
1.8520 
1.8507 

O.880I 
O.8799 
O.8798 

24 
25 
26 

0.4756 

"•4759 
0.47(11 

0.5407 
0.5411 
0.541I 

1.8495 

1.8482 
1.8469 

O.8796 
O.8795 
O.8794 

36 
35 
34 

23 

29 
30 

31 
32 
33 

0.4764 
O.4766 

0.4769 

0.5418 
0.5422 
0.5426 

t.8456 
1.8443 

1.S430 

O.8792 
O.879I 

33 
32 
3i 
30 
29 
28 
27 

0.4772 

0.5430 

i.-li' 

0.S7SS 

o.4774 
0.4777 
"•4779 

o.5433 
0-5437 
0.5441 

1.8405 

1.8392 
1-8379 

O.S787 
O.8785 
O.8784 

34 

35 
36 

0.4782 
O.4784 

0.4787 

0.5445 
0.5448 
o.5452 

1.8367 
1-8354 
1.8341 

O.S783 
O.8781 
O.8780 

26 

25 
24 

37 
3S 
39 
40 

4i 
42 
43 

0.4789 
0.4792 
0.4795 

0.5456 
0.5460 
0.5464 

1.8329 
1. 8316 
1-8303 

O.8778 
O.8777 
O.8776 

23 
22 
21 
20 

19 

18 

0.4797 

0.5467 

..S-j.,1 

0.8774 

0.4800 
0.4802 
0.4805 

o.547i 
0.5475 

0-5479 

1.8278 
1.8265 
1-8253 

"•s773 
0.8771 
0.8770 

44 
45 
46 

0.  r"7 
O.4810 
O.4S12 

0.5482 
O.5486 
0.5490 

1.8240 

1.8228 
1. 8215 

0.8769 
0.8767 
0.8766 

16 
15 
M 

47 

r 

4'/ 

50 

5 1 

52 
53 

O.4815 
O.4818 
0.4820 

0.5494 
0.5498 
0.5501 

1.8202 
1.8190 

1.S177 

0.8764 
0.8763 

13 
12 
11 
10 

9 

8 

"..p2.i 

0.5505 

I..-H.S 

M.S760 

O.4825 

0.5509 
O.5513 

o.55i7 

1.815a 

1. 8 1 40 

1. 8127 

«>-s75'i 

0.8757 
0.8756 

54 

55 
56 

0.4833 
O.4838 

1 1,  --  -  -j'  1 
0.5524 
0.5528 

1.8115 
1. 8103 
[.8090 

0.875! 
O.S753 
0.8752 

6 
5 
4 

:: 
58 
59 
80 

0.  r  \o 
0.4846 

"•5532 
"•5535 
0.5539 

1.8078 
t.8o6« 

1.8053 

0.8750 
0.8749 

0.S74S 

3 
2 

1 
II 

0.5543 

1.8040 

,,-7|(, 

Cob 

Cot 

Tan  :  Sin 

Sin 

Tan    ( 

3ot  |  Cos 

0 

I 

0.484S 

o.5543  1 

'(.4. 1 

0.8746 

(30 

59 

0.4851 

o.5547  1 

802S 

0.8745 

2 

0.4S53 

0.5551  1 

8016 

0.8743 

58 

3 

0.4S56 

o.5555  1 

8003 

0.8742 

57 

4 

0.4858 

0.5558  1 

799i 

0.8741 

56 

5 

0.4861 

0.5562  1 

7979 

0.S739 

55 

6 

0.4863 

0.5566  1 

7966 

0.8738 

54 

7 

0.4866 

0.5570  1 

7954 

0.8736 

53 

8 

0.4868 

o.5574  1 

7942 

0.8735 

52  •• 

9 
10 

II 

0.4871 

o.5577  1 

793" 

0.8733 

51 
50 
49 

0.4874 

0.5581   1 

7'M7 

0.8732 

0.4876 

"•55^5   1 

7905 

0.8731 

12 

0.4879 

0.5589   1 

7893 

0.8729 

48 

13 

0.4881 

o.5593   1 

788] 

0.8728 

47 

14 

0.4884 

0.5596   1 

7868 

0.8726 

46 

15 

0.4886 

0.5600   I 

7856 

0.8725 

45 

16 

0.4889 

0.5604   1 

7844 

0.S724 

44 

17 

0.4S91 

0.5  60S   1 

7832 

0.8722 

43 

18 

0.4894 

0.5612   1 

7820 

0.8721 

42 

19 

20 

21 

0.4896 

0.5616   1 

7808 

0.8719 

41 
40 
39 

0.4S99 

0.5619   I 

7796 

■o-i> 

0.4901 

0.5623   1 

7783 

0.-716 

22 

0.4904 

0.5627   1 

7771 

0.8715 

38 

23 

0.4907 

0.5631   1 

7759 

0.8714 

37 

24 

0.4909 

0.5635   I 

7747 

0.8712 

36 

25 

0.4912 

0.5639   1 

7735 

0.8711 

35 

26 

0.4914 

0.5642   1 

7723 

0.8709 

34 

27 

0.4917 

0.5646   1 

7711 

0.8708 

33 

28 

0.4919 

0.5650   1 

7699 

0.8706 

32 

29 
30 

31 

0.4922 

O.5654   1 

7!^7 

0.871 15 

31 
30 

29 

0.4924 

O.5658   1 

7"7- 

0.8704 

0.4927 

0.5662   1 

7663 

O.J702 

32 

0.4929 

0.5665   1 

7651 

0.8701 

33 

0.4932 

0.5669   1 

7639 

0.S699 

27 

34 

0.4934 

0.5673   1 

7627 

0.8698 

26 

35 

o.4937 

0.5677   1 

7615 

0.8696 

25 

36 

0-4939 

0.5681   1 

7603 

0.8695 

24 

37 

0.4942 

0.5685   1 

7591 

o>(pi)4 

23 

38 

o.4944 

0.5688   I 

7579 

0.8692 

22 

39 
40 
4i 

0.4947 

c>.5<»)2   1 

7567 

.  >.-(..)! 

20 

19 

0.4950 

c>.5<»)(i   1 

7?  =  " 

O.86S9 

0.4952 

O.5700   1 

7544 

O.8688 

42 

0.4955 

0.5704   1 

753-1 

0.S686 

18 

43 

0.4957 

0.5708   1 

7520 

0.8685 

17 

44 

0.4960 

0.5712   I 

7So8 

0.8683 

16 

45 

0.4962 

0.57I5   I 

74')'. 

0.8682 

1^ 

46 

0.4965 

0.5719   1 

74>? 

0.8681 

14 

47 

0.4967 

o.5723   I 

7473 

0.8679 

13 

48 

0.4970 

0.5727   1 

74<» 

0.8678 

12 

49 
50 
5i 

0.4972 

"■5731   1 

7449 

10 

9 

0.4975 

"-735   1 

7137 

0.8675 

"•4977 

"•5  739   > 

7426 

52 

0.4980 

"•5743   1 

74'4 

0.8672 

8 

53 

0.4982 

0.5746   1 

7402 

0.S670 

7 

54 

0.4985 

0.5750   I 

7391 

0.8669 

6 

55 

O.4987 

0-5754   1 

7379 

0.8668 

5 

56 

...  (.,.,.• 

o.5758   I 

7367 

0.8666 

4 

57 

O.4992 

0.5762   I 

7355 

0.8665 

3 

58 

o.4995 

O.5766   1 

7344 

0.8663 

2 

59 
60 

0.4997 

0.5770   1 

7332 

...MM, J 

1 
11 

n.51 

0.5774   1 

7321  !  0.8660 

Cos  1  Col   | 

Can  i  sin 

161     211       331 


IU° 


\  \  ii  1: 


w 


150     210°  *330° 


120°  210°  *300° 


30c 


Natural 


128 
31°       *121°  211    *301 


Sin       Tan 


0.5000 


0.5003 
0.5005 
0.5008 
0.5010 
0.5013 
0.5015 
0.5018 
0.5020 
0.5023 


0.5025 


0.5028 
0.5030 
0.5033 

0.5035 
0.5038 
0.5040 

0.5043 
0.5045 
0.5048 


0.5774 


o.5777 
0.5781 
0.5785 
0.5789 
o.5793 
o.5797 
0.5801 
0.5805 
0.5  80S 


Cot       Cos 


.7321 


0.5812 


0.5050 


0.5053 
0.5055 
0.5058 

0.5060 
0.5063 
0.5065 
0.5068 
0.5070 
0-5073 


0.5075 


0.5078 
0.5080 
0.5083 
0.5085 
0.5088 
0.5090 

0.5093 
0.5095 
0.5098 


0.5100 


0.5103 
0.5105 
0.5108 
0.5110 
0.5113 
o.5"5 
0.5118 
0.5120 
0.5123 


0.5816 
0.5820 
0.5824 
0.5828 
0.5832 
0.5836 
0.5840 
0.5844 
0.5847 


0.5851 


0.5855 
0.5859 
0.5S63 
0.5867 

0.5871 
0.5875 
0.5879 
0.5883 
0.58S7 


1.7309 
1.7297 
1.7286 
1.7274 
1.7262 
1-7251 

1.7239 

1.7228 
1.7216 


o.Si 


•7205 


I.7I93 
1. 7182 
L7I70 

I-7I59 
I-7I47 
I.7I36 
1. 7124 
I-7H3 
I. 7I02 


.7090 


I.7079 
I.7067 
I.7056 
I-7045 
I.7033 
I.7022 

I.70II 

I.6999 

1.6988 


o.S(.5.| 
0.8657 
0.8656 
0.8654 
0.8653 
0.8652 
0.8650 
0.8649 
0.S647 


0.S646 


0.8644 
0.8643 
0.8641 
0.8640 
0.8638 
0.8637 
0.8635 
0.8634 
0.8632 


0.8631 


0,5*90 


0.5894 
0.5898 
0.5902 
0.5906 
0.5910 
0.5914 
0.5918 
0.5922 
0.5926 


0.5030 


0.5125 


0.5128 
0.5130 
o.5i33 
o.5i35 
0.5138 
0.5140 

o.5i43 
o.5i45 
0.5148 


0.5150 


Cos 


o.5934 
0.5938 
0.5942 

o.5945 
o.5949 
o.5953 

o.5957 
0.5961 
0-5965 


o.50<>0 


C5973 
0.5977 
O.5981 

0.5985 
O.5989 
0.5993 

0.5997 
O.6001 
0.6005 


'•'■■*:: 


1.6965 
1.6954 
1.6943 
1.6932 
1.6920 
1.6909 
1.6898 
1.6887 
1.6875 


:.6S64 


1.6853 
1.6842 
1.6831 
1.6820 
1.6808 
1.6797 
1.6786 
1.6775 
1.6764 


•6753 


■  ■■ 


Cot 


1.6742 
1.6731 
1.6720 
1.6709 
1.6698 
1.6687 
1.6676 
1.6665 
1.6654 


0.8630 
0.8628 
0.8627 
0.862-5 
0.8624 
0.8622 
0.8621 
0.8619 
0.8618 


0.8616 


0.8615 
0.8613 
0.8612 
0.8610 
0.8609 
0.8607 
0.8606 
0.8604 
0.8603 


0.S601 


0.8600 
0.8599 
0.8597 
0.8596 
0.8594 
0.8593 
0.8591 
0.8590 
0.8588 


0.8587 


.6643 


Tan 


0.8585 
0.8584 
0.8582 
0.8581 
0.8579 
0.8578 
0.8576 
0.8575 
0.8573 


"•*57- 


S111 


Sin 

Tail 

Cot 

Cos 

II 

I 

3 

0-5150 
0.5153 
0.5155 
0.5158 

1 ,.(,.  109 

1.6643 

0.8572 

80 

59 
58 
57 

0.6013 
0.6017 
,  1.6020 

1.6632 
1. 662 1 
1.6610 

0.8570 
0.8569 
0.8567 

4 

5 

(. 

0.5160 
0.5163 
0.5165 

0.0024 
0.6028 

• 

1.6599 
1.6588 
1.6577 

0.8566 
0.8564 
0.8563 

56 

55 

54 

8 
') 
10 

II 

13 

0.5168 
0.5170 
0.5173 

O.6040 

0.6044 

1.6566 

1.6555 
1.6545 

0.8561 
0.8560 
0.8558 

53 
52 
5i 
50 

40 
48 
47 

0.5175 

0.(104  s 

1-653-4 

o.8557 

0.517* 
0.5180 
0.5183 

0.1,052 
0.6056 

1  i.dot.O 

1.6523 
1. 6512 

1  01 

0.8555 
0.8554 

14 

15 

Id 

0.5185 
0.5188 
0.5190 

0.6064 
0.6068 

0.6072 

1.6490 
1.6479 

1.6469 

0.8551 
0.8549 
0.8548 

46 
45 
44 

17 
18 
19 

20 
21 
22 

23 

0.5193 
0.5195 
0.5198 

O.6O76 
O.608O 
O.6084 

1.6458 
1.6447 
1.6436 

0.8546 
0.854I 
0.8543 

43 
42 
I' 
40 

39 

38 
37 

0.5200 

0.6088 

1.6426 

0.6542 

0.5203 
0.5205 
0.5208 

0.6092 
O.6O96 
O.6IOO 

1.6415 
1.6404 
1.6393 

0.S540 
0.8539 
0.8537 

24 

25 
26 

0.5210 
0.5213 
0.5215 

0.6I04 
O.6IO8 
0.6II2 

1.6383 

1.6372 
1. 636 1 

0.8536 
0.8534 

0.S532 

36 

35 
34 

27 
28 

29 
30 

31 
32 
33 

0.5218 
0.5220 

0.5223 

O.6II6 
0.6I20 

O.0I24 

1-6351 
1.6340 

1.6320 

0.8531 
0.8529 
0.852S 

33 
32 
3i 
30 
2g 
28 

0.5225 

0.6I28 

1.6310 

0.8526 

0.5227 
0.5230 
0.5232 

0.6I32 
O.6I36 
0.6I40 

1.6306 

1.6297 

I.62S7 

0.8525 
0.8523 
0.8522 

34 
35 
36 

0.5235 
0.5237 
0.5240 

O.0I44 
O.6I4S 
0.6I52 

1.6276 
1.6265 

1.6255 

0.8520 
0.8519 
0.8517 

26 

25 
24 

37 
38 
39 
40 
41 
42 
43 

0.5242 

0.5245 
0.5247 

O.6I56 
0.6l60 
0.6l64 

1.6244 

1.6234 
1.6223 

0.8516 
0.S514 
0.8513 

23 
22 
21 
20 

."1 
1- 
17 

0.5250 

O.6I6S 

1.6212 

0.8511 

0.5252 
0.5255 
0.5257 

,  0.6I72 
O.6I76 
0.6l80 

I.02O2 
I.6I9I 
I.6l8l 

0.8510 

0.8508 
0.8507 

44 

45 
46 

0.5260 

0.5262 
0.5265 

0.6l84 
0.6I88 
O.6I92 

1. 6l  70 
I.6160 

I.OI40 

0.8505 
0.8504 
0.8502 

K) 

15 

•4 

47 
48 
40 
50 

51 

52 
53 

0.5267 
0.5270 
0.5272 

O.6I96 
0.6200 
0.6204 

1. 6 1 30 
1.612S 
1.6118 

0.8500 

13 

12 
1 1 

in 

9 

8 

7 

0.5275 

0.6208 

1.6107 

0.8496 

0.5277 
0.5279 
0.5282 

0.62I2 
0.62I6 
0.6220 

1.6097 
1.6087 
1.6076 

0.8494 
0.8493 
0.8491 

54 
55 
56 

0.5284 
0.5287 
0.5289 

0.6224 
0.6228 
0.6233 

1.6066 
1.6055 

1.6045 

0.8490 
0.8  |-~ 
0.8487 

6 
5 
4 

57 
58 
59 
60 

0.5292 
0.5294 
0.5297 

0.6237 

0.624I 

1  0.6245 

1.6034 
[.6024 

1.6014 

0.8482 

3 

1 

0 

0.5200 

1  0.6249 

1.6003 

,,,-p. 

Cos    Cot 

Tan 

Sin 

*149°  239°  *329°      50° 


Natural 


58 


*148°  238     '328 


124 

•122°  212°  *302° 


82c 


Natural 


33e 


T23°  213°  *303c 


Sin 

Tan 

Cot 

Cos 

0 
2 

3 

0.5299 

0.1,241)  1 

6003 

0.8480 

60 

59 

58 
57 

0.5302 
0.5304 
0.5307 

0.6253  1 
0.6257  1 
0.6261  1 

5993 
5983 
5972 

0.8479 

0.8477 
0.8476 

4 
6 

0.5309 
0.5312 
0.5314 

0.6265  1 
0.6269  1 
0.6273  1 

5962 

5952 
594i 

0.8474 
0.8473 
0.8471 

56 

55 
54 

8 
9 
10 

ii 

12 

13 

0.5316 

0.5319 

0.3321 

0.6277  1 
0.6281  1 
0.6285  1 

5931 
5921 

591 1 

0.8470 
0.8468 
0.8467 

53 
52 
5i 
50 

49 

4s 

47 

0.5324 

0.0280    I 

5900 

0.8465 

0.5326 
0.5329 
0.5331 

0. (>_><, 3    I 
O.6297    I 
O.63OI    I 

5890 
5880 
5869 

0.8463 
0.8462 
0.8460 

14 

1 5 

1 6 

o.5334 
0.5336 
o.5339 

O.6305    I 
O.63IO    I 
O.63I4    I 

5859 
5849 
5839 

0.8459 
0.8457 
0.8456 

46 
45 
44 

l7 

iS 

19 
20 

21 

22 
23 

...5341 
o.5344 
0.5346 

O.63I8    I 
0.6322    I 
O.6326    I 

5829 
5818 
5808 

0.8454 

0.8453 

0.8451 

43 
42 
41 
40 

39 

38 

37 

0.5348 

O.633O    I 

5798 

0.8450 

o.535i 
o.5353 
0.5356 

O.6334    I 
O.6338    I 
O.6342    I 

5788 
5778 
5768 

0.8448 
0.8446 
0.8445 

24 

25 
26 

0.535S 
0.5361 
0.5363 

O.6346    I 
O.635O    I 
O.6354    I 

5757 
5747 
5737 

0.8443 
0.8442 
0.8440 

36 

35 
34 

27 

28 

29 
30 

32 
33 

0.5366 
0.5368 
o.537i 

O.6358    I 
O.6363    I 
O.6367    I 

5727 
5717 
5707 

0.8439 
0.S437 
0.8435 

33 
32 
3i 
30 
29 
28 
27 

o.5373 

O.637I    I 

5(>97 

0.8434 

u-5375 
P-5378 
0.5380 

0.6375    I 

O.6379    I 
O.6383    I 

5687 
5677 
5667 

0.S432 
0.8431 
0.8429 

34 
35 
36 

0.5383 
0.5385 
0.5388 

O.6387    I 
O.639I    I 
O.6395    I 

5657 
5647 
5637 

0.8428 
0.8426 
0.8425 

26 
25 
24 

37 
38 
39 
40 

41 

s 

0.5390 
0-5393 
o.5395 

O.6399    T 
O.64O3    I 

0.1,408    1 

5627 
5617 
5607 

0.8423 
0.8421 
0.8420 

23 

21 
20 

l9 

18 

17 

o.5398 

O.6412.   I 

5597 

0.841  8 

0.5400 
0.5402 
0.540! 

O.6416   I 
O.642O   I 
O.6424   I 

5587 
5577 
5567 

0.8417 
0.8415 
0.8414 

44 

45 
46 

0.5407 
O.5410 

0.5412 

O.6428   I 
O.6432   I 
O.6436   I 

5557 
5547 
5537 

0.8412 
0.8410 
0.8409 

16 
15 
14 

47 

48 
49 

50 

51 

52 
53 

0.5415 
O.5417 

0.5420 

(J.  6440   I 
O.6445    I 

O.6449    ' 

5527 
5517 
5507 

0.8407 
0.8406 

0.8404 

l3 
12 

1  1 
10 

9 

8 

7 

0.5  )_•_' 

O.6453   I 

5497 

0.8  \l)  '■, 

0.5424 
0.5427 
0.5429 

O.6457   I 
O.646I    I 
O.6465    I 

5487 
5477 
5468 

0.8401 
0.8399 
0.8398 

54 
55 
56 

<>o432 
•'■5434 
"-5437 

O.6469   I 
0.6473    I 
O.6478    I 

5458 
5448 
5438 

0.8396 
0.8395 
0.8393 

6 

5 
4 

57 
58 

0  |  9 
"-5442 

0 . 0  \  8  2    1 
O.6486    1 

5428 
54i8 

0.8391 

0.8390 

3 

80 

0.5444 

O.649O    1 

5408 

0.8  JS> 

1 
0 

0.5446 

0.64Q4    1 

53')') 

0.83S7 

Cos 

Col 

Pan 

Sin 

Sin 

Tan 

Cot 

Cos 

0 

I 

0.5446 

0.6494  1 

5399 

0.8387 
0.8385 

00 
59 

o.5449 

0.6498  1 

5389 

2 

0.5451 

0.6502  1 

5379 

0.8384 

58 

3 

b-5454 

0.6506  1 

5369 

0.8382 

57 

4 

0.5456 

0.651 1  1 

5359 

0.8380 

56 

5 

0.5459 

0.6515  1 

5350 

0.8379 

55 

6 

0.5461 

0.6519  1 

534o 

0.8377 

54 

7 

0.5463 

0.6523  1 

5330 

0.8376 

53 

8 

0.5466 

0.6527  1 

5320 

0.8374 

52 

9 

10 
11 

0.5468 

0.6531  1 

53" 

0.8372 

5i 
50 
49 

0.5471 

0.6536  1 

5301 

0.8371 

o.5473 

0.6540  1 

5291 

0.8369 

12 

0.5476 

0.6544  1 

5282 

0.8368 

48 

13 

0.5478 

0.6548  1 

5272 

0.8366 

47 

M 

0.5480 

0.6552  1 

5262 

0.8364 

46 

15 

0.5483 

0.6556  1 

5253 

0.8363 

45 

16 

0.5485 

0.6560  1 

5243 

0.8361 

44 

17 

0.5488 

0.6565  1 

5233 

0.8360 

43 

18 

0.5490 

0.6569  1 

5224 

0.8358 

42 

19 
20 
21 

o.5493 

0.6573  1 

5214 

0.8356 

41 
40 
39 

o.5495 

0.6577  1 

5204 

0.8355 

0.5498 

0.6581  1 

5195 

0.8353 

22 

0.5500 

0.6585  1 

5185 

0.8352 

38 

23 

0.5502 

0.6590  1 

5175 

0.8350 

37 

24 

0.5505 

0.6594  1 

5166 

0.8348 

36 

25 

0.5507 

0.6598  1 

5156 

0.8347 

35 

26 

0.5510 

0.6602  1 

5147 

0.8345 

34 

27 

0.5512 

0.6606  1 

5137 

0.8344 

33 

28 

0.5515 

0.6610  1 

5127 

0.8342 

32 

29 
30 
31 

0.5517 

O.6615   * 

5118 

0.S340 

31 
30 
29 

0.5519 

O.6619   x 

5108 

0.S339 

0.5522 

O.6623   I 

5099 

0.S337 

32 

0.5524 

O.6627   I 

5089 

0.8336 

28 

33 

0.5527 

O.663I   I 

5080 

0.8334 

27 

34 

0.5529 

O.6636   I 

5070 

0.8332 

26 

3^ 

0.5531 

O.664O   I 

5061 

0.8331 

25 

36 

o.5534 

O.6644   I 

5051 

0.S329 

24 

37 

0.5536 

O.6648   I 

5042 

0.8328 

23 

38 

o.5539 

O.6652   I 

5032 

0.8326 

22 

39 
40 
4i 

0.5541 

O.6657   I 

5023 

0.8324 

21 
20 
19 

o.5544 

O.6661    I 

5013 

0.8323 

0.5340 

O.6665   I 

5004 

0.8321 

42 

0.5548 

O.6669   I 

4994 

0.S320 

18 

43 

0.5551 

O.6673   I 

498§ 

0.8318 

17 

44 

o.5553 

O.6678   I 

4975 

0.8316 

16 

45 

0.5556 

0.6682   I 

4966 

0.8315 

15 

46 

0.5558 

O.6686   I 

4957 

0.8313 

14 

47 

0.5561 

O.669O   I 

4947 

0.831 1 

13 

4» 

0.5563 

O.6694   I 

W38 

0.8310 

12 

49 

50 

51 

0.5565 

0. (>(>(,()    1 

4928 

0.8308 

10 

9 

0.^08 

0.(1703    1 

49i9 

0.8307 

0.5570 

O.6707   I 

I'H" 

0.8305 

52 

0.5573 

O.67I  I    I 

4900 

0.8303 

8 

53 

0.5575 

O.6715   I 

4891 

0.8302 

7 

54 

0.5577 

O.672O   I 

4882 

(1.8  ?00 

6 

55 

0.5580 

O.6724   I 

1-7- 

O.S298 

5 

56 

0.5582 

0.0728    1 

4863 

0.8297 

4 

57 

0.5585 

O.6732   I 

4854 

3 

0.5587 

"•"737   ' 

4844 

O.8294 

2 

59 
60 

o.55<)o 

0.6741   I 

483  s 

0.8292 

1 
0 

0.551,2 

o.d745   1 

482(1 

0.8290 

Cos 

Cot   ! 

Pan 

Sin 

' 

NT     i:\:°  *32' 


:>7 


N  vi  URAL 


5(>° 


*146°  236'    *326 


*124°    214°  *304c 


34c 


Natural 


35°    *125°    215° 


125 

*305° 


Sin 

Tan 

Cot 

Cos 

0 

[ 

2 

3 

0.5592 

0.6745 

1.4826 

0.8290 

60 

59 

5S 
57 

0-5594 
o.5597 
o.5599 

0.6749 
0.6754 
0.6758 

1.4816 
1.4807 
1.4798 

U.S2.-«j 
O.8287 
O.8285 

4 
5 
6 

0.5602 
0.5604 
0.5606 

0.6762 
0.6766 
0.6771 

1.4788 

1-4779 
1.4770 

O.8284 
O.8282 
O.828I 

56 

55 
54 

7 
8 
9 

10 
1 1 

12 

13 

0.5609 
0.561 1 
0.5614 

0.6775 
0.6779 
0.6783 

1.4761 
I-475I 
1.4742 

O.8279 
0.8277 
O.8276 

53 
52 
51 
50 

49 

48 
47 

0.5616 

0.67S7 

1-4733 

0.S274 

0.5618 

0.5621 
0.5623 

0.6792 
0.6796 
0.6800 

1.4724 
I-47I5 
14705 

U.S272 
0.827I 
O.8269 

14 
15 
16 

0.5626 
0.5628 
0.5630 

0.6805 
0.6S09 
0.6813 

1.4696 
1.46S7 
1.4678 

O.8268 
O.8266 
O.8264 

46 
45 
44 

17 
18 
19 
20 
21 
22 
23 

0.5633 
0.5635 
0.5638 

0.6S17 
0.6S22 
0.6826 

1.4669 
1.4659 
1.4650 

O.8263 
0.826I 
O.8259 

43 
42 
41 
40 

39 

38 
37 

0.5640 

0.6830 

1-4641 

O.8258 

0.5642 
0.5645 
0.5647 

0.6834 
0.6839 
0.6843 

1.4632 
1.4623 
1-4614 

O.S256 
0.8254 
0.8253 

24 

25 
26 

0.5650 
0.5O52 
o.5654 

0.6847 
0.6851 
0.6856 

1.4605 

I.4596 
1.4586 

0.8251 
O.8249 
O.8248 

36 
35 
34 

27 
28 
29 
30 

31 
32 
33 

0.5657 
0.5659 
0.5662 

0.6860 
0.6864 
0.6869 

1-4577 
1.456S 
1-4559 

O.8246 
O.8245 

O.S243 

33 
32 
3i 
30 

29 
28 
27 

O.5664 

0.6873 

I4550 

O.S24I 

0.5666 
0.5669 
0.5671 

0.6S77 
0.68S1 
0.6S86 

M54I 

1-4532 
14523 

O.824O 
O.S238 
O.8236 

24 

35 
36 

o.5674 
0.5676 
0.5678 

0.6S90 
0.6894 
0.6899 

1.4514 

14505 
1.4496 

O.8235 
O.8233 
O.823I 

26 

24 

37 
38 
39 
40 

41 
42 
43 

0.5681 
0.5683 
0.5686 

0.6903 
0.6907 
0.69 1 1 

1.4487 
I.4478 
1.4469 

O.823O 
0  8228 
O.S226 

23 
22 
21 
20 

19 

18 

0.5688 

1 1.(19 10 

1.4460 

O.8225 

0.5690 
0.5693 
0.5695 

0.6920 

0.6924 
0.6929 

I-445I 
1.4442 
1-4433 

O.8223 
0.822I 
0.8220 

44 

45 

46 

0.5698 
0.5700 
0.5702 

0.6933 
0.6937 
0.6942 

1.4424 
I-44I5 
1.4406 

0.82I8 
0.82I6 
0.82I5 

16 
15 
14 

47 

4s 

49 
50 

5i 
52 

53 

0.5705 
0.5707 
0.5710 

0.6946 
0.6950 
0.6954 

1-4397 
14388 
1-4379 

0.82I3 
0.82II 
0.82IO 

13 

11 
10 

9 

8 

7 

0.5712 

0.6959 

14370 

0.8208 

0.57I4 
o.57i7 
0.57I9 

0.6963 
0.6967 
0.6972 

1.4361 
1-4352 
1-4344 

O.8207 
0.8205 
0.82C3 

54 
55 
56 

0.5721 
0.5724 
0.5726 

0.6976 
0.6980 
0.6985 

1-4335 
1.4326 
I43I7 

0.8202 
0.8200 
O.S198 

6 
5 
4 

57 
58 
59 
60 

0.5729 
0.573I 
0.5733 

0.6989 
0.6993 
0.6998 

14308 
1.4299 
1.4290 

O.8197 
O.8195 
O.8193 

3 
2 

0 

o.5736 

0.7002 

1.4281    1  0.8192 

Cos        Cot 

|    Tan         Sin 

' 

Sin    J   Tan 

Cot 

Cos 

11 

1 

0.57  56 

0.7002 

1.4281 

0.8192 

60 
59 

0.5738 

0.7006 

14273 

0.8190 

2 

0.5741 

0.701 1 

1.4264 

0.8188 

58 

3 

"■5743 

0.7015 

14255 

0.8187 

57 

4 

0.5745 

0.7019 

1.4246 

0.8185 

56 

5 

0.5748 

0.7024 

14237 

0.8183 

55 

6 

0.5750 

0.7028 

1.4229 

0.8181 

54 

7 

0.5752 

0.7032 

1.4220 

0.8180 

53 

8 

o.5755 

0.7037 

1.4211 

0.8178 

52 

9 

10 
11 

o.5757 

0.7041 

1.4202 

0.-17(1 

51 
50 
49 

11.57(10 

(j. 704(1 

14193 

'  j.-i  1 75 

0.^702 

0.7050 

1.4185 

0.8173 

12 

0.5764 

0.7054 

1. 4 1 76 

0.8171 

48 

13 

0.5767 

0.7059 

1.4167 

0.8170 

47 

14 

0.5769 

0.7063 

14158 

0.S168 

46 

15 

0.5771 

0.7067 

1.415° 

0.8166 

45 

16 

0.5774 

0.7072 

1.4141 

0.8165 

44 

17 

0.5776 

0.7076 

1.4132 

0.8163 

43 

18 

0.5779 

0.70S0 

1.4124 

0.8161 

42 

19 
20 
21 

0.5781 

0.70S5 

1.4115 

0.S160 

4' 
40 
39 

0.5783 

0.7089 

1. 4  I  Oil 

0.8158 

0.5786 

0.7094 

1.4097 

0.S156 

22 

0.5788 

0.7098 

1.4089 

0.S155 

38 

23 

0.5790 

0.7102 

1.4080 

0.8153 

37 

24 

0.5793 

0.7107 

1-4071 

0.81 51 

36 

25 

0.5795 

0.7111 

1 .401 .3 

0.8150 

35 

26 

0.5798 

0.7115 

14054 

0.8148 

34 

27 

0.5800 

0.7120 

1.4045 

0.S146 

33 

28 

0.5802 

0.7124 

14037 

0.8145 

32 

29 
30 

31 

0.5805 

0.7129 

1.4028 

0.8143 

3i 
30 

29 

0.5807 

0.7133 

1. 401 9 

0.8141 

0.5S09 

0.7137 

1. 401 1 

0.8139 

32 

0.5SI2 

0.7142 

I.4002 

0.S138 

28 

33 

0.5SI4 

0.7146 

1-3994 

0.S136 

27 

34 

0.5816 

0.7151 

I-3985 

0.8134 

26 

35 

0.5819 

0.7155 

1.3976 

0.8133 

2S 

36 

0.5821 

0.7159 

1.396S 

0.8131 

24 

37 

0.5824 

0.7164 

1-3959 

0.8129 

23 

38 

0.5826 

0.7168 

I-395I 

0.8128 

22 

39 
40 
4i 

0.5828 

0.7173 

1.3942 

0.8126 

21 

20 
19 

0.5831 

0.7177 

1-3934 

0.S124 

0.5833 

0.7181 

1.3925 

0.8123 

42 

0.5835 

0.7IS6 

1.3916 

0.8121 

18 

43 

0.5838 

0.7190 

1.3908 

0.S119 

17 

44 

0.5840 

0.7195 

1.3899 

0.81 17 

16 

4s) 

0.5842 

0.7199 

1.3891 

0.81 16 

15 

46 

0.5845 

0.7203 

1.3882 

0.8114 

4 

47 

0.5847 

0.7208 

1.3874 

0.S112 

13 

48 

0.5S50 

0.7212 

1.3865 

0.S111 

12 

49 
50 

si 

0.5852 

0.7217 

t.3857 

0.8109 

1 1 

10 
9 

0.5854 

0.7221 

1.3S4- 

0.8107 

0.5857     0.7226 

1.3840 

0.8106 

52 

0.5859 

0.72J30 

1-3831 

0.8104 

S 

53 

0.5861 

0.7234 

1.3S23 

0.8102 

7 

54 

0.5864 

0.7239 

1.3814 

0.8100 

6 

55 

0.5866 

0.7243 

1.3806 

0.S099 

5 

56 

0.5868 

0.7248 

I-3798 

0.8097 

4 

0.5S7I 

0.7252 

I-3789 

0.8095 

3 

58 

0.5873 

0.7257 

i-378i 

0.8094 

2 

59 
60 

0.5875 

0.7211] 

1-3772 

0.8092 

0 

0.720: 

1.3764     0.8090 

Cos 

Cot 

Tan        Sin 

145°  235"  *325°       00 


Natural 


54° 


*144°  234°  *324c 


126 
»126 


216°  *3i»6° 


36c 


Natural 


37 


n2-o   2170   *307o 


Sin  I  Tan 

Cot 

Cos 

0 

I 

0.587^  |  0.726s 

1.3764 

(,.-<„,<) 

60 

5Q 

0.7270 

1 1.8(  188 

2 

O.7274 

1-3747 

0.80S7 

*8 

3 

0.5SS5 

0.7279 

1-3739 

0.8085 

57 

4 

O.7283 

I-3730 

0.80S3 

<?6 

5 

O.7288 

1.3722 

0.80S2 

ss 

6 

0.7292 

I.37I3 

0.8080 

54 

0.7297 

1-3705 

0.S07S 

53 

3 

0.5897 

O.730I 

I.3697 

0.8076 

52 

9 
10 
11 

0.5899 

O.7306 

1.3668 

0.0075 

5i 
50 

49 

0.5901 

0.73IO 

1.3680 

0.0073 

0.5904 

0.73I4 

1.3672 

0.8071 

12 

0.5906 

0.73I9 

1.3663 

0.8070 

48 

13 

0.5908 

0.7323 

1.3655 

0.8068 

47 

14 

0.591 1 

O.7328 

1-3647 

0.S066 

46 

15 

0.5913 

0.7332 

1.3638 

0.8064 

45 

16 

0.5915 

0.7337 

1.3630 

0.8063 

44 

17 

0.5918 

0.734I 

1.3622 

0.8061 

43 

18 

0.5920 

O.7346 

1.3613 

0.8059 

42 

19 

20 
21 

0.5922 

"■735" 

1.3605 

0.8058 

4i 
40 
39 

0.5925 

"■735  5 

1-3597 

0.8056 

0.5927 

"■7359 

1.3588 

0.8054 

22 

0.5930 

0.7364 

i.358o 

0.8052 

38 

23 

0.5932 

0.7363 

1-3572 

0.8051 

37 

24 

o.5934 

0.7373 

I-3564 

0.8049 

36 

25 

o.5937 

0-7377 

1-3555 

0.8047 

35 

26 

0.5939 

0.7382 

1-3547 

0.8045 

34 

27 

0.5941 

0.7386 

1-3539 

0.8044 

33 

28 

0.5944 

o.739l 

I-353I 

0.8042 

32 

29 

30 
3i 

0.5946 

o.7395 

1.3522 

0.8040 

3i 
30 
29 

0.5948  1  1.7400 

I-35M 

O.8039 

0.5951 

O.7404 

1.3506 

0.8037 

32 

0.5953 

0.7409 

1.3498 

0.8035 

28 

33 

0.5955 

0.74I3 

1.3490 

0.8033 

27 

34 

0.5958 

0.7418 

1.3481 

0.8032 

26 

35 

0.5960 

0.7422 

1-3473 

0.8030 

25 

36 

0.5962 

0.7427 

I-3465 

0.8028 

24 

37 

0.5905 

0.7431 

1-3457 

0.S026 

23 

3S 

0.5967 

0.7436 

1-3449 

0.8025 

22 

39 

4(> 

41 

0.5969 

0.7440 

1-3440 

0.8023 

21 
20 
l9 

0.5972 

0.7445 

1-3432 

0.8021 

"■:■:  '74 

0.7449 

1-3424 

0.8019 

42 

O.5976 

o.7454 

1.3416 

0.8018 

t8 

43 

O.5979 

0.7458 

1.340S 

0.8016 

17 

44 

O.5981 

0.7463 

1.3400 

0.8014 

rfi 

45 

O.5983 

0.7467 

1-3392 

0.8013 

15 

4'' 

O.5986 

0.7472 

I-3384 

O.801 1 

14 

47 

O.5988 

0.7476 

1-3375 

0.8009 

13 

*8 

O.599O 

0.7481 

I-3367 

0.8007 

12 

49 

50 
5> 

0-5993 

0.7485 

1-3359 

0.8006 

1 1 
10 

9 

0-5995 

0.7490 

I-335I 

.,.Soo4 

0-5997 

"•7495 

1-3343 

0.0002 

52 

0.6000 

0.7499 

1-3335 

O.8000 

8 

53 

0.6002 

0.7504 

1-3327 

O.7999 

7 

54 

0.6004 

0.7508 

I-33I9 

O.7997 

6 

55 

0.6007 

0.75I3 

1-33" 

0-7995 

5 

5'' 

0.7517 

I-3303 

'J- 7993 

4 

57 

0.7522 

1-3295 

0.7992 

3 

5* 

0.7526 

I.3287  0.7990 

2 

59 

60 

0.6016 
0.6018 

"•7531 

0.7988 

I 

0 

,.7986 

Cos     Cut 

Tan  ;  Sin 

' 

Sin 

Tan 

Cot  |  Cos 

0 

I 

0.601 3 

0.7536 

1.3270 

0.79S6 

60 

59 

0.6020 

0.7540 

1.3262 

0.7985 

2 

0.6023 

0.7545 

1-3254 

0.7983 

S3 

3 

0.6025 

0.7549 

1.3246 

0.7981 

57 

4 

0.6027 

o.7554 

1.3238 

0-7979 

;(> 

5 

0.6030 

0.7558 

1.3230 

o.7978 

55 

6 

0.6032 

0.7563 

1.3222 

o.7976 

54 

7 

0.6034 

0.7568 

1-3214 

0-7974 

SI 

8 

0.6037 

0.7572 

1.3206 

0.7972 

52 

9 
10 

11 

0.6039 

0.7577 

1.3198 

0.7971 

5i 
50 
49 

0.6041 

0.7501 

1. 3190 

0.7969 

0.6044 

0.7586 

1.3182 

0.7967 

12 

0.6046 

0.7590 

1-3175 

0.7965 

4s 

13 

0.6048 

o.7595 

1-3167 

0.7964 

47 

14 

0.6051 

0.7600 

1-3159 

0.7962 

46 

*5 

0.6053 

0.7604 

1-3151 

0.7960 

4^ 

16 

0.6055 

0.7609 

1-3143 

o.7958 

44 

17 

0.6058 

0.7613 

i-3i35 

0.7956 

41 

18 

0.6060 

0.7618 

1.3127 

o.7955 

42 

19 
20 
21 

( 1.(11  il>2 

0.7623 

1-3119 

o.7953 

4i 
40 
39 

O.6065 

0.7627 

1.3m 

0.7951 

O.6067 

0.7632 

1.3103 

0.7949 

22 

O.6069 

0.7636 

1-3095 

0.7948 

38 

23 

O.607I 

0.7641 

1.3087 

0.7946 

37 

24 

O.6074 

0.7646 

1-3079 

6-7944 

36 

25 

O.6076 

0.7650 

1.3072 

0.7942 

35 

26 

O.6078 

0.765! 

1.3064 

0.7941 

34 

27 

O.608I 

0.7659 

1.3056 

0-7939 

hi 

28 

O.6083 

0.7664 

1.3048 

o.7937 

32 

29 
30 
.31 

O.6085 

O.6088 

0.7669 

1.3040 

0-7935 

31 
30 
29 

0.7673 

1.3032 

0.7934 

O.609O 

0.707s 

1.3024 

0.7932 

32 

O.6092 

0.7683 

1-3017 

0.7930 

28 

33 

O.6095 

0.7687 

1.3009 

0.7928 

27 

34 

O.6097 

0.7692 

1. 3001 

0.7926 

26 

35 

O.6099 

0.7696 

1.2993 

0.7925 

25 

36 

0.6IOI 

0.7701 

1.2985 

0.7923 

24 

37 

O.6IO4 

0.7706 

1.2977 

0.7921 

23 

38 

O.6106 

o.771o 

1.2970 

0.7919 

22 

39 
4U 

4i 

O.6108 

o.77i5 

1.2962 

0.7918 

21 
20 
19 

0.6l  1 1 

0.7720 

1.2954 

0.7916 

O.61I3 

0.7724 

1.2946 

0.7914 

42 

0.6II5 

0.7729 

1.293S 

0.7912 

18 

43 

0.61 1 8 

o.7734 

1. 2931 

0.7910 

17 

44 

0.6120 

0.7738 

1.2923 

0.7909 

16 

45 

0.6122 

o.7743 

1.2915 

0.7907 

15 

46 

0.6124 

o.7747 

1.2907 

0.7905 

14 

47 

0.6127 

o.7752 

1.2900 

0.7903 

13 

48 

0.6129 

o.7757 

1.2892 

0.7902 

12 

49 
50 

0.613] 

0.7701 

1.2884 

1  1.71)1  11  , 

10 

0.6134 

0.7766 

1.2876 

O.7898 

51 

0.6136 

"■7771 

1.2869 

0.781)6 

9 

52 

0.6138 

o.7775 

1.2861 

"■7S'M 

S 

53 

0.6141 

0.7780 

1-2853 

0.7893 

7 

54 

0.6143 

0.7785 

1.2846 

0.7891 

6 

55 

0.6145 

0.7789 

1.2838 

0.7889 

!? 

56 

0.6147 

0.7794 

1.2830 

0.7887 

4 

57 

0.6150 

o.7799 

1.2822 

0.7885 

3 

58 

0.6152 

0.7803 

1.2815 

O.7884 

2 

59 
60 

0.6154 

0.7808 

1.2S07 

O.7882 

0.7000 

0 

0.6157 

0.7S13 

1.2799 

Cos  .  Cot 

Tan    Sin 

143    2:;:: 


Natural 


►142    232 


*128°  218° 

*308° 

38° 

Natui 

' 

Sin  |  Tan 

Cot 

Cos 

0 

i 

2 

3 

0.6157 

0.7813 

1.2799 

0.7880 

60 

59 

58 

57 

0.6159 
0.6161 
0.6163 

0.7818 
0.7822 
0.7827 

1.2792 
1.2784 
1.2776 

0.7878 
0.7877 
0.7875 

4 

5 
6 

0.6166 
0.6168 
0.6170 

0.7S32 
0.7836 
0.7841 

1.2769 
1.2761 
1-2753 

0.7873 
0.7871 

0.7869 

56 

55 
54 

7 

S 

9 
10 

12 

13 

0.6173 
0.6175 
0.6177 

0.784*6 
0.7850 

0.7855 

1.2746 
1.2738 
1-2731 

0.786S 
0.7866 
0.7864 

53 
52 
51 
50 

49 
4S 
47 

0.6180 

0.7S60 

1.2723 

v.- 6(i2 

0.6182 
0.6184 
0.6186 

0.7865 
0.7869 
0.7874 

1-2715 
1.2708 
1.2700 

O.7860 
0.7859 
0.7857 

14 
15 
16 

0.6189 
0.6191 
0.6193 

0.7879 

0.7883 
0.7888 

1.2693 
1.26S5 
1.2677 

O.785! 
0.7853 
O.7851 

46 
45 
44 

17 
18 

19 

20 
21 

22 
23 

0.6196 
0.6198 
0.6200 

0.7893 
0.7898 
0.7902 

1.2670 
1.2662 
1.2655 

O.7850 
O.7848 
O.7846 

43 
42 
4i 
40 

39 

38 
37 

0.6202 

0.7907 

1.2647 

0.7844 

0.6205 
0.6207 
0.6209 

0.7912 
0.7916 
0.7921 

1.2640 
1.2632 
1.2624 

O.7S42 
O.7S41 
0.7839 

24 

25 
26 

0.62 1 1 
0.6214 
0.6216 

0.7926 
0.7931 
o.7935 

1.2617 
1.2609 
1.2602 

0.7832 
O.783! 
0.7833 

36 
35 
34 

27 
28 

29 
30 

31 
32 
33 

0.6218 
0.6221 
0.6223 

0.7940 
o.7945 
0.7950 

1.2594 

1.2587 
1-2579 

O.7832 
O.7830 

0.7828 

33 
32 
31 
30 
29 
28 
27 

0.6225 

0.7954 

1.2572 

0.7826 

0.6227 
0.6230 
0.6232 

0.7959 
0.7964 
0.7969 

1.2564 
1-2557 
1.2549 

0.7824 
0.7822 
0.7821 

34 
35 
36 

0.6234 
0.6237 
0.6239 

o.7973 
0.7978 
0.7983 

1.2542 
1.2534 
1.2527 

O.7S19 
O.7817 
O.7815 

26 

25 
24 

37 
38 
39 
40 

4i 
42 

43 

0.6241 
0.6243 
0.6246 

0.79S8 
0.7992 
0.7997 

1.2519 
1. 2512 
1.2504 

0.7813 
0.7812 
0.7810 

23 
22 
21 
20 

19 

18 

0.6248 

0.8002 

1.2497 

0.7808 

0.6250 
0.6252 
0.6255 

0.8007 
0.8012 
0.8016 

1.2489 
1.2482 
1.2475 

O.7806 
O.7804 
0.7802 

44 
45 
46 

0.6257 
0.6259 
0.6262 

0.8021 
0.8026 
0.8031 

1.2467 
1.2460 

1.2452 

O.7801 
0.7799 
0.7797 

16 
J5 
14 

47 
48 

49 
50 

5i 
52 

53 

0.6264 
0.6266 
0.6268 

0.8035 
0.8040 
0.8045 

1.2445 
1.2437 
1.2430 

0.7795 
0.7793 
O.7792 

13 
12 
11 
10 

9 

S 
7 

0.6271 

0.8050 

1.2423 

0.7790 

0.6273 
0.6275 
0.6277 

0.8055 
0.8059 
0.8064 

1-2415 
1.2408 
1. 2401 

0.7788 
0.7786 
O.77S4 

54 
55 
56 

0.6280 
0.6282 
0.6284 

0.8069 
0.8074 
0.8079 

1.2393 
1.2386 
1.2378 

0.7782 
0.7781 

0.7779 

6 
5 
4 

57 

5S 

-59 

60 

0.6286 
0.6289 
0.6291 

0.8083 
0.8088 
0.8093 

1-2371 
1.2364 
1.2356 

0-7777 
C7775 
0.7773 

3 
2 

1 
0 

0.6293 

0.8098 

1.2349 

0.7771 

Cos  |  Cot 

Tan 

Sin 

39c 


429°  219c 


127 

*30'J° 


' 

Sin  |  Tan  | 

Cot 

Cos 

0 

I 

0.6293 

0.S09S 

1-2349 

0.7771 

60 

59 

U.0295 

U.S103 

I.2342 

0.7770 

2 

0.6298 

0.8107 

1-2334 

0.7768 

58 

3 

0.6300 

0.8112 

1.2327 

0.7766 

57 

4 

0.6302 

0.8117 

1.2320 

0.7764 

56 

5 

0.6305 

0.8122 

1. 2312 

0.7762 

55 

6 

0.6307 

0.8127 

1.2305 

0.7760 

54 

7 

0.6309 

0.8132 

1.2298 

0-7759 

53 

8 

0.63 1 1 

0.8136 

1.2290 

o.7757 

52 

9 
10 

0.6314 

0.8141 

1.2283 

o.7755 

51 
50 

49 

0.6316 

0.6146 

1.2276 

0-7753 

0.6318 

0.8151 

1.2268 

o.775i 

12 

0.6320 

0.8156 

1. 2261 

o.7749 

4^ 

13 

0.6323 

0.8161 

1.2254 

0.7748 

47 

14 

0.6325 

0.8165 

1.2247 

0.7746 

46 

15 

0.6327 

0.8170 

1.2239 

o.7744 

45 

16 

0.6329 

0.8175 

1.2232 

0.7742 

44 

17 

0.6332 

0.8180 

1.2225 

0.7740 

43 

iS 

0.6334 

0.8185 

1.2218 

o.7738 

42 

19 

20 
21 

0.6336 

0.8190 

1. 2210 

o.7737 

41 

40 

39 

0.6338 

0.8195 

1.2203 

o.7735 

0.6341 

0.8199 

1.2196 

o.7733 

22 

0.6343 

0.8204 

1.2189 

o.773i 

38 

23 

0.6345 

0.8209 

1.2181 

0.7729 

37 

24 

0.6347 

0.8214 

1.2174 

0.7727 

36 

25 

0.6350 

0.8219 

1. 2167 

0.7725 

35 

26 

0.6352 

0.8224 

1. 2160 

0.7724 

34 

27 

0.6354 

0.8229 

I-2I53 

0.7722 

33 

28 

0.6356 

0.8234 

1. 2145 

0.7720 

32 

29 
30 

31 

0.6359 

0.8238 

1.2138 

0.7718 

31 
30 

29 

0.6301 

0.8243 

1.2131 

0.7716 

0.6363 

0.8248 

1. 2124 

0.7714 

32 

0.6365 

0.8253 

1.2117 

o.77i3 

28 

33 

0.6368 

0.8258 

1. 2109 

0.7711 

27 

34 

0.6370 

0.8263 

1. 2102 

0.7709 

26 

35 

0.6372 

0.8268 

1.2095 

0.7707 

25 

36 

0.6374 

0.8273 

1.2088 

0.7705 

24 

37 

0.6376 

0.8278 

1.2081 

0.7703 

23 

38 

0.6379 

0.8283 

1.2074 

0.7701 

22 

39 
40 

41 

0.6381 

0.82S7 

1.2066 

0.7700 

21 
20 
19 

0.6383 

0.8292 

1.2059 

0.7698 

0.6385 

0.8297 

1.2052 

0.7696 

42 

0.6388 

0.8302 

1.2045 

0.7694 

iS 

43 

0.6390 

0.8307 

1.2038 

0.7692 

17 

44 

0.6392 

0.8312 

1. 203 1 

0.7690 

16 

45 

0.6394 

0.8317 

1.2024 

0.7688 

15 

46 

0.6397 

0.8322 

1.2017 

0.7687 

M 

47 

0.6399 

0.8327 

1.2009 

0.7685 

13 

48 

0.6401 

0.8332 

1.2002 

0.7683 

12 

49 
50 

51 

0.6403 

0.8337 

I.I995 

0.7681 

II 
lit 

9 

0.6406 

0.8342 

1.1988' 

0.7679 

0.6408 

0.8346 

1.1981 

0.7677 

52 

0.6410 

0.8351 

1. 1974 

0.7675 

S 

S3 

0.6412 

0.8356 

1. 1967 

0.7674 

7 

54 

0.6414 

0.8361 

1. 1960 

0.7672 

6 

55 

0.6417 

0.8366 

1. 1953 

0.7670 

5 

56 

0.6419 

0.8371 

1. 1946 

0.7668 

4 

57 

0.6421 

0.S376 

1 -1939 

0.7666 

3 

58 

0.6423 

0.8381 

1. 1 932 

0.7664 

2 

59 
60 

0.6426 

0.8386 

1-1925 

0.7662 

1 

0 

„ 

0.6428  j  0.8391 

1.191S 

0.7000 

Cos  |  Cot 

Tan  |  Sin 

1 

>141°  231°  *321° 


5r 


Natural 


5UC 


440°  230°  *320° 


•130°     220°  *310°      40C 


Natural 


41°    *131°    221°  *311' 


sin   Tan 

Clot   1  loa 

0 

I 

2 

3 

1.1518 

0.7660 

60 

59 

58 

57 

0.6430 
0.6432 

0.6435 

0.8396 
0.8401 
0.8406 

1.1910 

1. 1903 
1. 1896 

0.7659 
0.7657 
0.7655 

4 
5 
6 

0.6437 
0.6439 
0.6441 

0.S411 
0.S416 
0.8421 

1. 1889 
1.1S82 
1-1875 

0.7653 
0.7651 
0.7649 

56 

55 
54 

9 
10 

1 1 

12 

c.6443 
0.6446 
0.6448 

0.8426 
0.8431 

0^436 

1. 1868 
1.1861 
1. 1854 

0.7647 
0.7645 

"■7"44 

53 
S2 
51 
50 

49 
48 

47 

0.6450 

0.8441 

1.1S47 

0.7642 

0.6452 
0.6455 
0.6457 

0.8446 

0.8451 
0.8456 

1.1 840 
1-1833 
1. 1826 

,,.71,40 
O.7638 
0.7636 

1 6 

0.6459 
0.6461 
0.6463 

0.8461 
0.8466 
0.8471 

1.1S19 
1.1812 
1.1S06 

0.7634 
0.7632 
0.7630 

46 

45 
44 

i  7 

iS 

19 
20 
21 

22 

23 

0.6466 
0.6468 
0.6470 

0.8476 
0.8486 

1. 1799 
1. 1792 
1. 1785 

0.7629 
0.7627 
O.7625 

43 
42 
41 
40 

39 
38 
37 

0.6472 

0.8491 

1-1778 

0.7623 

0.6475 
0.6477 
0.6479 

0.8496 
0.8501 
0.8506 

1.1771 
1. 1764 
1.1757 

O.7621 
O.7619 
0.7617 

24 

25 

26 

0.6481 
0.6483 
0.6486 

0.8511 
0.8516 
0.8521 

1-1750 

1-1743 
1. 1736 

0.7615 
0.7613 
0.7612 

36 
35 
34 

2  7 
28 

29 

30 

31 
32 
33 

0.6488 
0.6490 
0.6492 

0.8526 
0.S531 
0.8536 

1-1729 
1. 1722 
1-1715 

0.7610 
0.7608 
0.7606 

33 
32 
3i 
30 
29 
28 

0.6494 

0.S541 

1 . 1 708 

O.7604 

0.6497 
0.6501 

0.S546 
0.8551 
0.8556 

1.1702 
1. 1695 
1. 1688 

0.7602 
0.7600 
0.7598 

34 
35 
36 

0.6503 
0.6506 
0.6508 

0.8561 
0.8566 
0.8571 

1.16S1 
1-1674 
1. 1667 

0.7596 
0.7595 
0-7593 

26 

25 
24 

37 

38 
39 
40 

41 
42 
43 

0.6510 
0.6512 
0.6514 

0.8576 
0.8581 
0.8586 

1. 1660 
1-1653 
1.1647 

0.759I 
0.7589 
0.7587 

23 

21 

20 

19 

18 
17 

0.6517 

0.8591 

1. 1640 

0.7585 

0.6521 
0.6523 

0.8596 
0.8601 
0.8606 

1.1633 
1. 1626 
1.1619 

0.7583 
0.7581 
0-7579 

44 

45 
46 

0.6525 
0.6528 
0.6530 

0.861 1 
0.8617 
0.8622 

1.1612 
1. 1606 

I-I599 

0.7578 
0.7576 
0-7574 

16 
15 

47 
48 
49 

BO 

51 
52 
53 

0.6532 
0.6534 
0.6536 

0.8627 
0.8632 
0.8637 

1-1592 
1-1585 
I-I578 

0.7572 
0-7570 

13 

1 1 
10 

9 
8 

7 

0.6539 

0.8642 

1. 1571 

,,.7?M, 

"•"541 

.,.-1,17 
0.8652 

1. 1565 
I-I558 
i-i55i 

O.7564 
0.7562 

O.7560 

54 

55 
56 

0.6552 

0.8662 
0.8667 

1-1544 

1. 1538 
i-i53i 

0-7559 

"•7555 

6 

? 
4 

57 
58 
59 
80 

• 

O.8678 
0.8683 
0.8688 

[.1524 

1.1  =  17 
1.1510 

0-7553 
o.755l 
0-7549 

3 

(i 

1.1504 

■•■::  17 

Cob   Col 

Tan   sin 

111 


Sin 


0.6561 


0.6563 
0.6565 
0.6567 
0.6569 
0.6572 
0.6574 
0.6576 
0.6578 
0.6580 


0.6583 


0.6585 
0.6587 
0.6589 
0.6591 
0.6593 
0.6596 
0.6598 
0.6600 
0.6602 


0.6604 


0.6607 
0.6609 
0.661 1 
0.6613 
0.6615 
0.6617 
0.6620 
0.6622 
0.6624 


0.6626 


0.6628 
0.6631 
0.6633 
0.6635 
0.6637 
0.6639 
0.6641 
0.6644 
0.6646 


0.6648 


0.6650 
0.6652 
0.6654 
0.6657 
0.6659 
0.6661 
0.6663 
0.6665 
0.6667 
( 1.1,1,7, , 


0.6672 
0.6674 

0.6676 
0.6678 
0.6680 
0.6683 

,,.,,0-7 

<>.(><  >$9 
Q.o6()l 


Cos 


Tan 


0.8693 


0.8698 
0.8703 
0.8708 
0.8713 
0.8718 
0.8724 
0.8729 
0.8734 
0.8739 


0.8744 


0.8749 
0.8754 
0.8759 
0.8765 
0.8770 
0.8775 
0.8780 
0.8785 
0.8790 


( i.>-,)i. 


0.8801 
0.8806 

0.8811 
0.8816 
0.8821 
0.8827 
0.8832 
0.8837 
0.8842 


">M7 


0.8852 
0.8858 
0.8863 
0.8868 
0.S873 
0.8878 
0.8884 
0.8889 
0.8894 


o.SS,|() 


O.8904 
O.89IO 
O.8915 
O.8920 
O.8925 
O.893I 
O.8936 
O.894I 
O.8946 
O.8952 


O.8957 

o.S.,(i2 
0.89(17 
O.8972 

0.S07S 

o.s,,-.; 
0.8988 

0.8999 
0.9004 


Cot 


\  \  1  1  RaL 


Col 


5<>4 


1497 
1490 
1483 
1477 
1470 
1463 
1456 
1450 
1443 


1436 


1430 
1423 
1416 

1410 

1403 
1396 

1389 
1383 
1376 


1369 


1363 
1356 
1349 
1343 
1336 
1329 
1323 
1316 
1310 


Cos 


0-7547 


1296 
1290 
1283 
1276 
1270 
1263 
1257 
1250 
1243 


1237 


1230 
1224 
1217 
1211 
1204 
1197 
[191 
[184 


1171 


II65 
1158 
1152 
"45 

U39 
1  1  32 

1126 
1119 
1 1 13 


0-7545 
0-7543 
0-754I 

0-7539 
o.7538 
o.7536 
0-7534 
o.7532 
0.7530 


0.7528 


0.7526 
0.7524 
0.7522 

0.7520 
0.7518 
0.7516 

0751! 
o-75i3 
0.7511 


0.7509 


0.7507 
0.7505 
0.7503 
0.7501 
0.7499 
0.7497 

0-7495 

"■7493 
-■>-749i 


'■74"" 


[06 


0.74S8 
0.7486 
0.7484 
0.7482 
0.7480 
0.7478 
0.7476 
"•7474 
0.7472 


"■74  7" 


O.7468 
O.7466 
0.7464 

0.7403 

0.7461 

"■74?'» 
0.7457 
"•7455 
0.7453 
o-745' 
o.7449 
"•7447 
"•7445 
"•7443 
o.744i 
O.7439 

"■7137 
0-7435 

"■74  33 


"■743' 


318° 


*132°  222°  *312c 


42c 


Natural 


43°       *133°  223c 


129 
*313° 


Sin 

Tan  | 

Cot 

Cos 

0 

0.6691 

0.9004 

1.1106 

0.7431 

t'O 

59 

58 

57 

I 

2 

3 

0.6693 
0.6696 
0.6698 

0.9009 
0.9015 
0.9020 

I.I  IOO 

I. 1093 
I. 1087 

0.7430 
0.7428 
0.7426 

4 

5 
6 

0.6700 
0.67*02 
0.6704 

0.9025 
0.9030 
0.9036 

I. 1080 
1. 1074 
1. 1067 

0.7424 
0.7422 
0.7420 

56 
55 
54 

7 
8 

9 
10 

12 

13 

0.6706 
0.6709 
0.671 1 

0.9041 
0.9046 
0.9052 

1.1061 

I. 1054 

I. 1048 

0.7418 
0.7416 
0.7414 

53 
52 
5i 
50 

49 

48 
47 

0.6713 

0.9057 

1.1041 

0.7412 

0.6715 
0.6717 
0.6719 

G.IJ002 

0.9067 

0.9073 

1.1035 
1. 1028 
1. 1022 

0.7410 
0.7408 
0.7406 

15 
16 

0.6722 
0.6724 
0.6726 

0.9078 
0.9083 
0.9089 

1.1016 
1. 1009 
1. 1003 

0.7404 
0.7402 
0.7400 

46 
45 
44 

17 
iS 
19 
20 

21 
22 

2 

0.6728 
0.6730 
0.6732 

0.9094 
0.9099 

0.9105 

1.0996 
1.0990 
1.0983 

0.7398 
0.7396 
o.7394 

43 
42 
41 
40 

39 

38 

37 

0.6734 

0.91 10 

1.0977 

0.7392 

0.6737 
0.6739 
0.6741 

0.9115 

0.9121 
0.9126 

1. 097 1 
1.0964 
1.0958 

0.7390 

0.7388 
0.7387 

24 

25 
26 

0.6743 
0.6745 
0.6747 

0.9131 
0.9137 
0.9142 

1.0951 
1.0945 
1.0939 

0.7385 
0.7383 
0.7381 

36 

35 
34 

27 
23 

29 

30 
3i 

32 

33 

0.6749 
0.6752 

0.6754 

0.9147 
0.9153 

0.915s 

1.0932 
1.0926 
1.0919 

o.7379 
o.7377 

o.7375 

33 
32 
31 

30 

29 

28 
27 

0.6756 

0.9163 

1.0913 

o.7373 

0.675S 
0.6760 
0.6762 

0.9169 

0.9174 
0.9179 

1.0907 
1.0900 
1.0894 

0.7371 
0.7369 
0.7367 

34 

35 
36 

0.6764 
0.6767 
0.6769 

0.9185 

0.9190 

0.9195 

1.0888 
1.0881 
1.0875 

0.7365 
0.7363 
0.7361 

26 

25 
24 

37 
38 
39 
40 

4i 

42 
43 

0.6771 
0.6773 
0.6775 

0.9201 
0.9206 
0.9212 

1.0869 
1.0862 
1.0856 

o.7359 
o.7357 
o.7355 

23 
22 
21 
20 

19 
18 

17 

0.6777 

0.9217 

1.0850 

o.7353 

0.6779 
0.67S2 
0.6784 

0.9222 
0.9228 

0.9233 

1.0843 
1.0837 
1.0831 

0.7351 
o.7349 
o.7347 

44 
45 
46 

0.67S6 
0.6788 
0.6790 

0.9239 

0.9244 
0.9249 

1.0824 
1.0818 

1.0S12 

o.7345 
o.7343 
0.7341 

16 
15 
14 

47 
48 
49 
50 

5i 

52 
53 

0.6792 
0.6794 
0.6797 

0.9255 
0.9260 
0.9266 

1.0805 
1.0799 
I-0793 

o.7339 
o.7337 

o.7335 

13 

11 
10 

9 

8 
7 

0.6799 

0.9271 

1.0786 

o.7333 

0.6801 
0.6803 
0.6805 

0.9276 
0.9282 
0.9287 

1.0780 
1.0774 
1.0768 

0.7331 
0.7329 
0.7327 

54 
55 
56 

0.6807 
0.6809 
0.6S11 

0.9293 

0.9298 

0.9303 

1.0761 
I-0755 
1.0749 

0.7325 
0.7323 
0.7321 

6 

5 
4 

57 
58 
59 
60 

0.6814 
0.6816 
0.6818 

0.9309 

0.9314 

0.9320 

1.0742 
1.0736 
1.0730 

o.73T9 
0.7318 
0.7316 

3 
0 

0.6S20 

0.9325 

1.0724 

0.7314 

Cos  |  Cot 

Tan 

Sin 

' 

Sin  J  Tan  ) 

Cot  |  Cos 

0 
1 

0.6820 

0.9325 

1-0724 
1.0717 

0.7314 
0.7312 

60 

59 

0.6822 

0.933I 

2 

0.6824 

O.9336 

1.0711 

0.7310 

58 

3 

0.6826 

0.934I 

1.0705 

0.7308 

57 

4 

0.6828 

0.9347 

1 .0699 

0.7306 

56 

5 

0.6831 

0.9352 

1.0692 

0.7304 

55 

6 

0.6833 

0.9358 

1.0686 

0.7302 

54 

7 

0.6835 

O.9363 

1.0680 

0.7300 

53 

8 

0.6837 

O.9369 

1.01,74 

0.7298 

52 

9 

1U 
1 1 

0.6839 

0.9374 

I  .U( .(.."! 

0.721,0 

51 
50 
49 

0.6841 

O.9380 

1. 066 1 

0.720; 

0.6843 

O.9385 

I.O655 

0.7292 

12 

0.6845 

O.939I 

LO649 

0.7290 

48 

13 

0.6848 

O.9396 

1 .0643 

0.72-- 

47 

14 

0.6850 

O.9402 

I.O637 

0.7286 

46 

15 

0.6852 

O.9407 

I.O63O 

0.7204 

45 

16 

0.6854 

0.94I3 

I.0624 

0.7282 

44 

17 

0.6856 

O.9418 

1. 061 8 

0.7280 

43 

IS 

0.6858 

O.9424 

1. 061 2 

0.7278 

42 

19 
20 
21 

0.6860 

O.9429 

1 .0606 

0.7276 

4i 
40 
39 

0.6862 

0.9435 

1.0599 

0.7274 

0.6865 

O.944O 

I.0593 

0.7272 

22 

0.6S67 

O.9446 

1.0587 

0.7270 

.38 

23 

0.6869 

O.945I 

1.0581 

0.7268 

37 

24 

0.6871 

0.9457 

I.0575 

0.7266 

36 

25 

0.6873 

O.9462 

1.0569 

0.7264 

35 

26 

0.6875 

O.946S 

1.0562 

0.7262 

34 

27 

0.6877 

0.9473 

1.0556 

0.7260 

33 

28 

0.6879 

0.9479 

1.0550 

0.7258 

32 

29 
30 
31 

0.6S81 

O.94S4 

1.0544 

0.7256 

3i 
30 
29 

0.6SS4 

0.9490 

1.053S 

0.7254 

0.6886 

0-9495 

1.0532 

0.7252 

32 

0.6888 

O.95OI 

1.0526 

0.7250 

28 

33 

0.6890 

O.9506 

1.0519 

0.7248 

27 

34 

0.6892 

O.9512 

1-0513 

0.7246 

26 

35 

0.6894 

0.95I7 

1.0507 

0.7244 

25 

36 

0.6896 

0.9523 

1.0501 

0.7242 

24 

37 

0.6898 

O.9528 

1-0495 

0.7240 

23 

38 

0.6900 

0.9534 

1.0489 

0.723S 

22 

39 
40 
41 

0.6903 

O.954O 

1.0483 

'  '-7-3" 

21 
20 

19 

0.6905 

0-9545 

1.0477 

0.7234 

0.6907 

0.955I 

1.0470 

O.7232 

42 

0.6909 

0.9556 

1.0464 

O.7230 

IS 

43 

0.69 1 1 

O.9562 

1.0458 

0.722S 

17 

44 

0.6913 

O.9567 

1.0452 

0.7226 

16 

45 

0.6915 

0.9573 

1.0446 

0.7224 

1 5 

46 

0.6917 

O.9578 

1.0440 

0.7222 

M 

47 

0.6919 

O.9584 

I.0434 

O.7220 

"3 

48 

0.6921 

O.959O 

1.0428 

0.721S 

12 

49 
50 

51 

0.6924 

0.9595 

1.0422 

0.7216 

I  I 

10 
9 

0.6926 

O.96  'I 

1. 041 1. 

0.7214 

0.6928 

O.9606 

1.0410 

O.7212 

52 

0.6930 

O.9612 

1.0404 

0.7210 

S 

53 

0.6932 

O.9618 

1 .039S 

0.7208 

7 

54 

0.6934 

O.9623 

1.0392 

0.7206 

6 

55 

0.6936 

O.9629 

1.0385 

O.7203 

5 

56 

0.6938 

0.9634 

I.0379 

0.7201 

4 

57 

0.6940 

O.9640 

1 -03  73 

O.7199 

3 

58 

0.6942 

O.9646 

1.0367 

0.7197 

2 

59 
60 

0.6944 

O.965I 

1.0361 

0.7195 

I 

0 

0.6947  1  0.9657 

I.0355 

0.7I93 

COS   ;   Cot 

Tan 

Sin 

*3i-; 


Natural 


4<>c 


*136°  226°  *316c 


130 


Natural   44°  *134 

0  224°  *314° 

1 

Sin  |  Tan  |  Cot  !  Cos 

0- 

0.6947  0.9057 

1.0355  1  0.7193 

60 

59 

58 
57 

3 

0.6949 
0.6951 
0.6953 

0.9663 
0.9668 
0.9674 

1 -0349 
1 -0343 
I-0337 

0.7191 
0.71  B9 
0.7187 

4 
5 
6 

0.6955 
0.6957 
0.6959 

0.9679 
0.9685 
0.9691 

1 .0331 

1.0325 
1. 03 19 

0.7185 
0.71S3 
0.71S1 

56 

55 
54 

7 
8 
Q 

0.6961 
0.6963 
0.6965 

0.9696 
0.9702 
0.9708 

1.0313 
1.0307 

1.0301 

0.7179 
0.7177 
0.7175 

S2 
5i 
50 

49 

48 
47 

10 

0.6967 

0.9713 

1.0295 

0.7173 

II 

12 

13 

0.(1970 
0.6972 
0.6974 

c.9719 
0.9725 
0.9730 

1.0289 
1.0283 
1.0277 

0.7171 
0.7169 
0.7167 

14 
15 
16 

0.6976 
0.6978 
0.6980 

0.9736 
0.9742 
0.9747 

1.0271 
1.0265 
1.0259 

0.7165 
0.7163 

0.7161 

46 

45 
44 

17 
18 
19 
20 
21 
22 
23 

0.6982 
0.6984 
0.6986 

0.9753 
0.9759 
0.9764 

1.0253 
1.0247 
1.0241 

0.7159 
0.7157 
0.7155 

43 
42 
4i 
40 

39 

38 
37 

0.6988 

0.9770 

1.0235 

0.7153 

0.6990 
0.6992 
0.6995 

0.9776 
0.9781 

0.97S7 

1.0230 
1.0224 
1.0218 

0.7151 
0.7149 
0.7147 

24 

25 
26 

0.6997 
0  6999 
0.7001 

0.9793 
0.9798 
0.9804 

1.0212 
1.0206 
1.0200 

0.7145 
0.7143 
0.7141 

36 
35 
34 

27 
28 
29 
30 
31 
32 
33 

0.7003 
0.7005 
0.7007 

0.9810 
0.9816 

0.9S21 

1.0194 

1.0188 
1.0182 

0.7139 
0.7137 

0.7135 

33 
32 
3i 
30 

29 

28 

0.7009 

0.9827 

1.0176  1  0.7133 

0.7011 
0.7013 
0.7015 

0.9833 
0.9838 
0.9S44 

1.0170 
1.0104 
1.0158 

0.7130 
0.7128 
0.7126 

34 
35 
36 

0.7017 
0.7019 
0.7022 

0.9850 
0.9856 
0.9861 

1.0152 
1.0147 
1.0141 

0.7124 
0.7122 
0.7120 

26 
25 
24 

37 
38 
39 
40 

4i 
42 

43 

0.7024 
0.7026 

0.7028 

0.9867 
0.9873 
•0.9879 

1-0135 
1.0129 
1.0123 

0.7118 
0.7116 
0.7114 

23 

20 

19 

18 
17 

0.7030 

0.9884 

1...117 

0.7112 

0.7032 
0.7034 
0.7036 

0.9890 
0.9896 
0.9902 

I.OIII 

1.0105 
1.0099 

0.7110 
0.710S 
0.7106 

44 
45 
46 

0.7038 
0.7040 
0.7042 

0.9907 

0.9913 
0.9919 

1.0094 
1.0088 
1.0082 

0.7104 
0.7102 
0.7100 

16 
15 
14 

47 
48 
49 
50 

51 

52 

53 

0.7044 
0. 7046 
0.7048 

0.9925 
0.9930 
0.9936 

1.0076 
1.0070 
1.0064 

0.7098 
0.7096 
0.7094 

13 

1 1 
10 

9 

S 
7 

0.7050 

0.9.142 

1.0058 

0.701,2 

0.7053 
0.7055 
0.7057 

0.9948 

0.9954 
0.9959 

1.0052 

1.0047 
1. 004 1 

0.7000 
0.7088 
0.70S5 

54 

55 
56 

0.7059 
0.7061 
0.7063 

0.9965 
0.9971 
0.9977 

1.0035 
1.0029 
1.0023 

0.7083 
0.70S1 
0.7079 

6 
5 
4 

57 
58 
59 
00 

0.7067 
0.7069 

0.9988 
0.9994 

[.0017 

1. 001 2 
1  .coo6 

0.7077 
0.7075 

0.7073 

3 
2 

1 
0 

0.7071 

1 .0000 

1 ,( 1 

,,.;,  171 

Cos  ■  Cot   Tan  ;  Sin 

:<i:> 


4.50     Natura] 


131 


VI 

TABLE  OF   SQUARES, 

CUBES 

,  SQUARE   ROOTS  AND  CUBE 

,  ROOTS 

WHOLE 

NUMBERS  FROM  1  TO  1020 

The  numbers  are  given  in    the  col 

umns  headed  N,   their  squares, 

cubes,  square  roots  and  cube  roots  respectively  in 

the  columns  headed  N2, 

N3 

t/n  and  ^n 

0 

—60 

N 

N2 

N3 

l/N 

rs 

N 

N2 

N3 

l/N 

fN 

0 

i 

O 

0 

0.0000 

0.0000 

30 
31 

900 

27000 

5-4772 

3-1072 

! 

1 

1. 0000 

1 .0000 

961 

29791 

5.5678 

3.I4I4 

2 

4 

8 

1.4142 

1-2599 

32 

1024 

32768 

5-6569 

3.I748 

3 

9 

27 

1. 7321 

1.4422 

33 

1089 

35937 

5-7446 

3-2075 

4 

16 

64 

2.0000 

1.5874 

34 

1156 

39304 

5.8310 

3.2396 

5 

25 

125 

2.2361 

1. 7100 

35 

1225 

42875 

5-9IOI 

3-27II 

6 

36 

216 

2-4495 

1.8171 

36 

1296 

46656 

6.0000 

3:30I9 

7 

49 

343 

2.6458 

1.9129 

37 

1369 

50653 

6.0828 

3.3322 

8 

64 

512 

2.8284 

2.0000 

38 

1444 

54872 

6.1644 

3.3620 

9 
10 
ii 

81 

729 

3.0000 

2.0801 

39 
40 
41 

1521 

59319 

6.2450 

3.3912 

100 

1000 

3.1623 

2.1544 

1600 

64000 

6.3246 

3.4200 

121 

1331 

3.3166 

2.2240 

1681 

68921 

6.4031 

3.4482 

12 

144 

1728 

3.4641 

2.2894 

42 

1764 

74088 

6.4807 

3-476o 

13 

169 

2197 

3.6056 

2.3513 

43 

1849 

79507 

6-5574 

3.5034 

14 

196 

2744 

3-7417 

2.4101 

44 

1936 

85184 

6.6332 

3.5303 

15 

225 

3375 

3.8730 

2.4662 

45 

2025 

91125 

6.7082 

3-5569 

16 

256 

4096 

4.0000 

2.5198 

46 

2116 

97336 

6.7823 

3-5830 

17 

289 

49r3 

4-1231 

2.5713 

47 

2209 

103823 

6.8557 

3.6088 

18 

324 

5832 

4.2426 

2.6207 

48 

2304 

110592 

6.9282 

3-6342 

19 
20 
21 

361 

6859 

4-3589 

2.6684 

49 
50 

5i 

2401 

1 1 7649 

7.0000 

3-0593 

400 

8000 

4.4721 

2.7144 

2500 

125000 

7.07 1 1 

3.(1840 

441 

9261 

4.5826 

2.7589 

2601 

132651 

7.1414 

3.70^4 

22 

484 

10648 

4.6904 

2.8020 

52 

2704 

140608 

7.2111 

3-7325 

23 

529 

12167 

4-7958 

2.8439 

53 

2809 

148877 

7.2801 

3-7563 

24 

576 

13824 

4.8990 

2.8845 

54 

2916 

157464 

7-3485 

3.7798 

25 

625 

15625 

5.0000 

2.9240 

55 

3025 

166375 

7.4162 

3.8030 

26 

676 

17576 

5.0990 

2.9625 

56 

3136 

175616 

7.4833 

3-8259 

27 

729 

19683 

5.1962 

3.0000 

57 

3249 

185193 

7.5498 

3-8485 

28 

784 

21952 

5.29I5 

3.0366 

58 

3364 

I95"2 

7.6158 

3.8709 

29 
30 

841 

24389 

5-3852 

3.0723 

59 
60 

348i 

205379 

7.68 1 1 

3-8930 

900 

2  7000 

5-4772 

3.1072 

3600 

216000 

7.7460 

3-9*49 

N 

N3 

X3 

l-'N 

fN 

N 

H" 

H> 

V  N 

f  N 

132 


60- 

-180 

X 

N1 

N5 

l  N 

fN 

N 

X2 

N3 

l/N 

r!x 

60 

6i 

3600 

216000 

7.7460 

120 

121 

14400 

172S000 

10.954! 

4-9324 

3721 

226981 

7.8102 

3-9365 

1 464 1 

1771561 

11.0000 

4.9461 

62 

3844 

238328 

7.8740 

J-9579 

122 

14SS4 

1815848 

11.0454 

4.9597 

63 

3969 

250047 

7-9373 

3-9791 

123 

15129 

1860867 

11.0905 

4-9732 

64 

1096 

262144 

8.0000 

4.0000 

124 

15376 

1906624 

"•1355 

4.9866 

65 

4225 

274625 

3.0623 

4.0207 

125 

15625 

1953125 

11.1S03 

5.0000 

66 

4356 

287496 

8.1240 

4.0412 

126 

15876 

2000376 

11.2250 

5.0133 

67 

4489 

300763 

8.1854 

4-0615 

127 

16129 

2048383 

11.2694 

5.0265 

68 

4624 

314432 

8.2462 

4.0817 

128 

16384 

2097152 

"•3137 

5-0397 

69 
70 
7i 

4761 

328509 

8.3066 

4.1016 

129 
130 
131 

1 664 1 

21466S9 

n-3578 

5.0528 

4900 

343000 

8.3666 

4.1213 

16900 

2197000 

1 1. 401 8 

5.0658 

5041 

357')'  1 

8.4261 

4.140S 

17161 

224S091 

"•4455 

5.0788 

72 

5184 

373248 

8.4853 

4.1602 

132 

17424 

2299968 

11.4891 

5-0916 

5329 

389017 

8.5440 

4-1793 

133 

17689 

2352637 

11.5326 

5-1045 

74 

5476 

405224 

8.6023 

4.1983 

134 

17956 

2406104 

11.5758 

5-1172 

5625 

421875 

8.6603 

4.2172 

135 

18225 

2460375 

11. 6190 

5-1299 

76 

5776 

438976 

8.7178 

4-2358 

136 

18496 

2515456 

11.6619 

5.142b 

77 

5929 

456533 

8.775o 

4-2543 

137 

18769 

2571353 

11.7047 

5-1551 

78 

6084 

474552 

8.8318 

4.2727 

138 

19044 

2628072 

H-7473 

5.1676 

79 
80 
81 

6241 

493039 

8.8882 

4.2908 

139 
140 

Mi 

19321 

2685619 

11.7898 

5.1801 

6400 

512000 

8.9443 

4.3089 

19600 

2744000 

11.8322 

5-1925 

6561 

53I44I 

9.0000 

4.3267 

19SS1 

2803221 

11.8743 

5.2043 

82 

6724 

551368 

9-0554 

4-3445 

142 

20164 

2863288 

1 1. 91 64 

5.2171 

83 

6889 

571787 

9.1 104 

4-3621 

i43 

20449 

•  2924207 

11.9583 

5-2293 

S4 

7056 

592704 

9.1652 

4-3795 

144 

20736 

2985984 

12.0000 

5-2415 

85 

7225 

614125 

9.2195 

4.3968 

145 

21025 

3048625 

12.0416 

5-2536 

86 

7396 

636056 

9.2736 

4.4140 

146 

21316 

3112136 

12.0830 

5.2656 

87 

7569 

658503 

9-3274 

4-43IO 

147 

21609 

3176523 

12.1244 

5-2776 

88 

7744 

681472 

9.3808 

4.4480 

148 

21904 

3241792 

12.1655 

5.2896 

89 
90 

91 

704969 

O.4340  4-4647 

149 
150 

I5I 

22201 

3307949 

12.2066   5.301 

8lOO 

729000   9.481! 

22500 

3375OO0 

12.2474   r-3'33 

8281 

753571 

9-5394 

4-4970 

22S01 

3442951 

12.2882  5-3251 

92 

8464 

778688 

9-5917 

4-5144 

152 

23104 

3511808 

12.3288 

5-3368 

93 

8649 

804357 

9-6437 

4-5307 

153 

23409 

3581577 

12.3693 

5.3485 

94 

8836 

830584 

9-6954 

4-5463 

i54 

23716 

3652264 

12.4097 

5.3601 

95 

9025 

857375 

9.7468 

4.5629 

'55 

24025 

3723875 

12.4499 

5-3717 

96 

9216 

884736 

9.7980 

4-5789 

156 

24336 

3796416 

12.4900 

5\3832 

97 

9409 

912673 

9.8489 

4-5047 

157 

24649 

3869893 

12.5300 

VJ 

98 

9604 

941 192 

9.8995 

4.0104 

158 

24964 

3944312 

12.5698 

5.4061 

99 
100 
101 

9801 

970299 

9.9499 

4.6261 

r59 
160 
161 

25281 

4019679 

12.6095 

5-4175 

1 0000 

1 '  ii 1 K  > 

1  <  1.0000 

4.6416 

25600 

4U()ln  i(  h  1 

12.6491 

5.42S8 

10201 

1030301 

10. 0  [()i) 

4.6570 

25921 

4I7328I 

12.6886 

5.4401 

102 

10404 

1061208 

10.0995 

4.6723 

162 

26244 

4251528 

12.7279 

5-4514 

103 

10609 

1092727 

10.1489 

4-6S75 

163 

26569 

4330747 

12.7071 

5.4626 

104 

10816 

1 124864 

10.1980 

4.7027 

164 

26896 

4410944 

12.8062 

-■4737 

105 

11025 

"57625 

10.2470 

4-7177 

,05 

27225 

4492125 

106 

11236 

1191016 

10.2956 

4.732*) 

166 

27556 

4574296 

u  384 1 

'"7 

1 1 449 

1225043 

10.344' 

4-7475 

167 

27SS9 

4657463 

[2.9228 

108 

1  [664 

1259712 

10.3923 

4.7622 

168 

2S224 

4741632 

[2  »6l§ 

[09 

111) 

1  1  1 

11881 

[295029 

10.4403 

Mm, 

170 

171 

28561 

48268O9 

13.0000 

12100 

1 33 1 OOO 

10.4SS1 

1  :  H  l 

28900 

mi  3 

13-0384!  ! 

12321 

1367631 

10.5357 

4.S059 

29241 

50002 1 1 

[3.0767 

;.."<>5 

1 12 

1  1.04928 

10.5830 

4.8203 

172 

29584 

50S844S 

13-1140 

5-56I3 

n  | 

12769 

1442897 

10.6301 

1.8346 

i73 

29929 

5'777'7 

[3.1529 

5.5721 

114 

1  2996 

1481544 

10.0771 

4.8488 

174 

30276 

5268024 

[3.1909 

- 

"5 

13225 

1520875 

[O.7238 

t.862g 

i75 

30625 

5359375 

1  J. 22  88 

5-5934 

[l6 

13456 

1560896 

I0.7703 

4-s7  7" 

[76 

30976 

5451776 

[3.2665 

5.6041 

'  '7 

13689 

16016]  3 

CO.8167 

i77 

31329 

5545233 

1  >.  1041 

Il8 

[6430  )2 

1.9049 

178 

5639752 

[3.3417 

5.6252 

MM 

120 

1  |H.i 

1685159 

10.9087 

179 
180 

32041 

5735339 

13-3791 

5-6357 

'I  V" 

1  72.H000 

10.9545" 

V2   |<"' 

=,S3-'OIM> 

13.4164 

5.0462 

1  N 

V 

N;' 

1  n  |  r1  n 

N 

JS'2 

Xs 

1  N 

9   N 

180 

—300 

N  | 

N2  | 

X3 

•a  1   f'N 

N  | 

X2 

X3 

1  N 

fN 

180 

181 

32400 

5832000 

13.4164 

5.6462 

240 
241 

57600 1 

13824000 1 

15.VC9 

6.2145 

32761 

5929741 

134536 

5-6567 

^S.,Si 

i399752i 

15-5242 

6.2231 

182 

33124 

6028568 

134907 

5.6671 

242 

58564 

14172488 

I5-5563 

6.2317 

183 

33489 

6128487 

13-5277 

5-6774 

243 

59049 

14348907 

15-5885 

6.2403 

184 

33856 

6229504 

13-5647 

5-6877 

244 

59536 

14526784 

15.6205 

6.2488 

185 

34225 

6331625 

13.6015 

5.6980 

245 

60025 

14706125 

15-6525 

6.2573 

186 

34596 

6434856 

13.6382 

5-7083 

246 

60516 

14886936 

15-6844 

6.2658 

187 

34969 

6539203 

13.6748 

5-7185 

247 

61009 

15069223 

15-7162 

6.2743 

188 

35344 

6644672 

13-7113 

5-7287 

248 

61504 

15252992 

15.7480 

189 
190 
191 
192 

35721 

6751269 

13-7477 

5.7388 

249 
250 

251 

62001 

15438249 

15-7797 

b.2912 

-*6ioo 

6859000 

13.7840 

5-7489 

62500 

15625000 

I5-8H4 

6.2996 

36481 

6967871 

13.8203 

5-7590 

63001 

15813251 

15-8430 

6.3080 

36864 

7077888 

13.8564 

5-7690 

252 

63504 

16003008 

I5-8745 

6.3164 

193 

37249 

7189057 

13.8924 

5-7790 

253 

64009 

16194277 

15.9060 

6.3247 

194 

37636 

7301384 

13.9284 

5.7890 

254 

64516 

16387064 

15-9374 

6.3330 

195 
196 

38025 

7414875 

13.9642 

5-7989 

255 

65025 

16581375 

15.9687 

6.3413 

38416 

7529536 

14.0000 

5.8088 

256 

65536 

16777216 

16.0000 

6.3496 

197 
198 

38809 

7645373 

I4-0357 

5.8186 

257 

66049 

16974593 

16.0312 

6-3579 

39204 

7762392 

14.0712 

5.8285 

258 

66564 

17173512 

16.0624 

6.3661 

199 
200 

39601 

7880599 

14.1067 

5-8383 

259 
260 

261 

67081 

17373979 

16.0935" 

6-3743 

40000 

8000000 

14.1421 

5.8480 

67600 

17576000 

16.1245 

6.3825 

40401 

8 1 2060 1 

14.1774 

5-8578 

68121 

i777958i 

I6.I555 

6.3907 

202 

40804 

8242408 

14.2127 

5-8675 

262 

68644 

17984728 

16.1864 

6.3988 

203 

41209 

8365427 

14.2478 

5-8771 

263 

69169 

18191447 

16.2173 

6.4070 

204 

41616 

8489664 

14.2829 

5.8868 

264 

69696 

18399744 

16.2481 

6.41 5 1 

205 

42025 

8615125 

14.3178 

5.8964 

265 

70225 

18609625 

16.2788 

6.4232 

206 

42436 

8741816 

I4-3527 

5-9059 

266 

70756 

18821096 

16.3095 

6.4312 

207 

42849 

8869743 

I4-3875 

5-9155 

267 

71289 

19034163 

16.3401 

6.4393 

208 

43264 

8998912 

14.4222 

5-9250 

268 

71824 

19248832 

16.3707 

6.4473 

209 
210 
211 

43681 

9129329 

14.4568 

5-9345 

269 
270 
271 

72361 

19465109 

16.4012 

6-4553 

44100 

9261000 

14.4914 

5-9439 

72900 

ig683OO0 

16.4317 

6.4633 

44521 

9393931 

14.5258 

5-9533 

73441 

19902511 

16.4621 

6.4713 

212 

44944 

9528128 

14.5602 

5.9627 

272 

73984 

20123648 

16.4924 

6.4792 

213 

45309 

9663597 

14-5945 

5-9721 

273 

74529 

20346417 

16.5227 

6.4872 

214 

45796 

9800344 

14.6287 

5.9814 

274 

75076 

20570824 

16.5529 

6.4951 

215 

46225 

9938375 

14.6629 

5-9907 

275 

75625 

20796S75 

16.5831 

6.5030 

2l6 

46656 

10077696 

14.6969 

6.0000 

276 

76176 

21024576 

16.6132 

6.5108 

217 

47089 

10218313 

14.7309 

6.0092 

277 

76729 

21253933 

16.6433 

6.5187 

218 

47524 

10360232 

14.7648 

6.0185 

278 

77284 

21484952 

16.6733 

6.5265 

219 

220 
221 

47961 

10503459 

14.7986 

6.0277 

279 
280 
281 

77841 

21717639 

16.7033 

6-5343 

48400 

10648000 

14.8324 

6.0368 

78400 

21952000 

16.7332 

6.5421 

48841 

10793861 

14.8661 

6.0459 

78961 

22188041 

16.7631 

6-5499 

222 

49284 

10941048 

14.8997 

6.0550 

282 

79524 

2242576S 

16.7929 

6-5577 

223 

49729 

11089567 

14-9332 

6.0641 

283 

80089 

22665187 

16.8226 

6.5654 

224 

50176 

11239424 

14.9666 

6.0732 

284 

80656 

22906304 

16.8523 

6.5731 

225 

50625 

1 1 39062 5 

15.0000 

6.0822 

285 

81225 

23149125 

16.8819 

6.580S 

226 

51076 

II543I76 

I5-0333 

6.0912 

286 

81796 

23393656 

16.9115 

6.5885 

227 

51529 

11697083 

15.0665 

6.1002 

287 

82369 

23639903 

16.941 1 

6.5962 

228 

51984 

11852352 

15.0997 

6.1091 

288 

82944 

23887S72 

16.9706 

6.6039 

229 
230 
231 

52441 

12008989 

15-1327 

6.1180 
6.1269 

289 
290 
291 

83521 

24137569 

17.0000 

6.6115 

52900 

1 2167000 

15.1658 

84100 

24389000 

17.0294 

6.6191 

5336i 

12326391 

15.1987 

6.1358 

84681 

246421 71 

17.0587 

6.6267 

232 

53824 

12487168 

15-2315 

6.1446 

292 

85264 

2489708S 

17.0880 

6.6343 

233 

54289 

12649337 

15-2643 

6.1534 

293 

85849 

25153757 

17.1172 

6.6419 

234 

54756 

1 28 1 2904 

15.2971 

6.1622 

294 

86436 

254121S4 

17.1464 

6.6494 

235 

55225 

12977875 

I5-3297 

6.1710 

295 

87025 

25672375 

17.1756 

6.6569 

236 

55696 

13144256 

15-3623 

6.1797 

296 

87616 

25934336 

17.2047 

6.6644 

237 

56169 

13312053 

I5-3948 

6.1885 

297 

88209 

26198073 

17-2337 

6.6719 

238 

56644 

13481272 

154272 

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S  I  (II  U  II 

729000001 

;,!.,  .in  11 

9.(15  19 

N 

N*      N3 

V  N   |  f   N 

N 

1  * 

N»       vN 

f  N 

139 


900- 

-102C 

N  |  N2     Ns 

l/N  |  fN 

*| 

N2 

N» 

900 
go  I 

810000 

729000000 

30.0000 

9-6549 

960 
961 

921600 

884736000 

30.9839 

9.8648 

811801 

731432701 

30.0167 

9-6585 

923521 

887503681 

31.0000 

9.8683 

902 

813604 

733870808 

30.0333 

9.6620 

962 

925444 

890277128 

31.0161 

9.8717 

903 

815409 

736314327 

30.0500 

9.6656 

963 

927369 

893056347 

31.0322 

9-875I 

904 

817216 

738763264 

30.0666 

9.6692 

964 

929296 

895841344 

31-0483 

9.8785 

905 

819025 

741217625 

30.0832 

9.6727 

965 

931225 

898632125 

31-0644 

9.8819 

906 

820836 

743677416 

30.0998 

9.6763 

966 

933156 

901428696 

31.0805 

9.8854 

907 

822649 

746142643 

30.1164 

9.6799 

967 

935089 

904231063 

31.0966 

9.8888 

908 

824464 

748613312 

30.1330 

9.6834 

968 

937024 

907039232 

31.1127 

9.8922 

909 
910 
911 

826281 

751089429 

30.1496 

9.6870 

969 
970 

97i 

938961 

909 S 53209 

31.1288 

9-8956 

828100 

75357IOOO 

30.1662 

9.6905 

940900 

912673000 

31-1448 

9.8990 

829921 

756058031 

30.1828 

9.6941 

942841 

915498611 

31.1609 

9.9024 

912 

831744 

758550528 

30.I993 

9.6976 

972 

944784 

918330048 

31.1769 

9.9058 

9*3 

8335^9 

761048497 

30.2159 

9.7012 

973 

946729 

921167317 

31.1929 

9.9092 

914 

835396 

763551944 

30.2324 

9.7047 

974 

948676 

924010424 

31.2090 

9.9126 

9*5 

837225 

766060875 

30.2490 

9.7082 

975 

950625 

926859375 

31.2250 

9.9160 

916 

839056 

768575296 

30.2655 

9.7118 

976 

952576 

929714176 

31.2410 

9.9194 

917 

840889 

771095213 

30.2820 

9-7153 

977 

954529 

932574833 

31.2570 

9.9227 

918 

842724 

773620632 

30.2985 

9.7188 

978 

956484 

935441352 

31-2730 

9.9261 

919 
920 
921 

844561 

776151559 

30.3150 

9.7224 

979 
980 
981 

958441 

938313739 

31.2890 

9-9295 

846400 

778688000 

30.33I5 

9-7259 

960400 

941 192000 

31.3050 

9.9329 

848241 

781229961 

30.3480 

9.7294 

962361 

944076141 

31.3209 

9-9363 

922 

850084 

783777448 

30.364I 

9-7329 

982 

964324 

946966168 

31-3369 

9.9396 

923 

851929 

786330467 

30.3809 

9-7364 

983 

966289 

949862087 

31-3528 

9.9430 

924 

853776 

788889024 

30.3974 

9.7400 

984 

968256 

952763904 

31.3688 

9.9464 

925 

855625 

791453125 

30.4138 

9-7435 

985 

970225 

955671625 

31-3847 

9-9497 

926 

857476 

794022776 

30.4302 

9.7470 

986 

972196 

958585256 

31.4006 

9-9531 

927 

859329 

796597983 

30.4467 

9-7505 

987 

974169 

961504803 

31.4166 

9-9565 

928 

861184 

799178752 

30.4631 

9-7540 

988 

976144 

964430272 

314325 

9.9598 

929 
930 
93i 

863041 

801765089 

30.4795 

9-7575 

989 
990 
991 

978121 

96736 1  (1O9 

31.4484 

9.9632 

864900 

804357000 

30.4959 

9.7610 

980100 

970299001 1 

31.4643 

9.9666 

S66761 

806954491 

30.5123 

9-7645 

9820S1 

973242271 

31.4802 

9.9699 

932 

868624 

809557568 

30.5287 

9.7680 

992 

984064 

976191488 

31.4960 

9-9733 

933 

870489 

812166237 

30.5450 

9-7715 

993 

986049 

979146657 

31-5119 

9.9766 

934 

872356 

814780504 

30.5614 

9-7750 

994 

988036 

982107784 

31-5278 

9.9800 

935 

874225 

817400375 

30.5778 

9-7785 

995 

990025 

985074875 

31-5436 

9-9833 

936 

876096 

820025856 

30.594I 

9.7819 

996 

992016 

988047936 

31-5595 

9.9866 

937 

877969 

822656953 

30.6105 

9-7854 

997 

994009 

991026973 

31-5753 

9.9900 

938 

879844 

825293672 

30.6268 

9.7889 

998 

996004 

99401 1992 

3i-59ii 

9-9933 

939 
940 
941 

881721 

827936019 

30.6431 

9.7924 

999 
1000 
1001 

99S001 

997002999 

31.6070 

9.9967 

883600 

830584000 

30.6594 

9-7959 

1 000000 

1 000000000 

31.6228 

10.0000 

885481 

833237621 

30.6757 

9-7993 

1002001 

1003003001 

31.6386 

10.0033 

942 

887364 

835896888 

30.6920 

9.8028 

1002 

1004004 

1006012008 

31.6544 

10.0067 

943 

889249 

838561807 

30.7083 

9.8063 

1003 

1006009 

1009027027 

31.6702 

10.0100 

944 

891136 

841232384 

30.7246 

9.8097 

1004 

1008016 

1 01 2048064 

31.6860 

10.0133 

945 

893025 

843908625 

30.7409 

9-8132 

1005 

1010025 

1015075125 

31.7017 

10.0166 

946 

894916 

846590536 

30.757I 

9.8167 

1006 

1012036 

1018108216 

3I-7I75 

10.0200 

947 

896809 

849278123 

30.7734 

9.8201 

1007 

10 1 4049 

1021147343 

31-7333 

10.0233 

948 

89S704 

851971392 

30.7896 

9.8236 

1008 

1016064 

1024192512 

31.7490 

10.0266 

949 
950 

951 

900601 

854670349 

130.8058 

9.8270 

1009 
1010 
ion 

1018081 

1027243729 

31.7648 

10.0299 

902500 

857375ooo 

30.8221 

9.8305 

1020100 

1030301000 

31.7805 

10.0332 

904401 

860085351 

30.8383 

9-8339 

I022I2I 

1033364331 

31.7962 

10.0365 

952 

906304 

862801408 

30.8545 

9-8374 

1012 

IO24144 

1036433728 

31.8119 

10.0398 

953 

908209 

865523177 

30.8707 

9.8408 

1013 

IO26169 

1039509197 

31.8277 

10.0431 

954 

910116 

868250664 

30.8869 

9-8443 

1014 

IO28196 

1042590744 

3I-8434 

10.0465 

955 

912025 

870983875 

30.9031 

9-8477 

1015 

1030225 

104567S375 

31.8591 

10.0498 

956 

9*3936 

873722816 

30.9192 

9-8511 

1016 

1032256 

1048772096 

31.8748 

10.0531 

957 

915849 

876467493 

30.9354 

9.8546 

1017 

IO34289 

1051871913 

31.8904 

10.0563 

958 

917764 

879217912 

30.9516 

9.8580 

101S 

IO36324 

1054977832 

31.9061 

10.0596 

959 
960 

919681  881974079 

30.9677 

9.8614 

1019 
1020 

IO3836I 

1058089859 

31.9218 

10.0629 

921600  1  884736000 

30.9839 

9.8648 

IO404OO 

1061 208000 

31-9374 

10.0662 

N 

X2     N3 

l/N 

fN 

N 

X2 

»• 

/N 

fN 

140 


"VII 

TABLE  OF 

FACTORS 

COMPUTING  PROBABLE  ERRORS. 

// 

•6745 

J  -6745 

•6745 

j    -6745 
\/  n  —  \ 

n 

.6745 

j    .6745 

•6745 
\/n—l 

j    .6745 
i    (i  —  i 

^  »i(n— l) 

]/«(n— 1) 

\'  n(n— 1) 

)/n(n— 1) 

40 
41 

0.01 71 

8.23241 

0.1080 

9.03344 

0.0167 

8.22155 

0.1066 

9.02795 

2 

0.4769 

9.67846 

0.6745 

9.82898 

42 

0.0163 

8.21096 

0  1053 

9.02258 

3 

0.2754 

9.43990 

0.4769 

9.67846 

43 

0.0159 

8.20062 

0.1041 

9-OI735 

-1 

0.1947 

9.28938 

0.3894 

9.59041 

44 

0.0155 

8.19051 

0.1029 

9.01224 

5 

0.1508 

9.17846 

0.3372 

9-52795 

45 

0.0152 

8.18064 

0.1017 

9.00725 

6 

0.1231 

9.09041 

0.3016 

9.47949 

46 

0.0148 

8.17099 

0.1005 

9.00237 

7 

0.1041 

9.01735 

0.2754 

9.43990 

47 

0.0145 

8.16155 

0.0994 

8.99760 

8 

0.0901 

8.95488 

0.2549 

9.40643 

48 

0.0142 

S.15231 

0.0984 

8.99283 

9 
10 

0.0795 

8.90031 

0.2385 

9-37743 

49 
50 
5i 

0.0139 

8.14326 

0.0974 

8.98835 

0.07 1 1 

8.85185 

0.2248 

9-35I85 

0.0136 

8.13439 

0.0964 

8.98388 

0.0643 

8.80828 

0.2133 

9.32898 

0.0134 

8.12571 

0.0954 

8-97949 

12 

0.0587 

8.76869 

0.2029 

9.30828 

52 

0.0131 

8.11719 

0.0944 

8.97519 

13 

0.0540 

8.73241 

0.1947 

9.28938 

53 

0.0128 

8.108S4 

0.0935 

8.97097 

14 

0.0500 

8.69894 

0.1871 

9.27200 

54 

0.0126 

8.10064 

0.0926 

8.96684 

15 

0.0465 

8.66787 

0.1803 

9.25591 

55 

0.0124 

8.09260 

0.0918 

8.96278 

i6 

0.0435 

8.63887 

0.1742 

9.24093 

56 

0.0122 

8.08470 

0.0900 

8.95S79 

1- 

0.0409 

8.61169 

0.1686 

9.22692 

57 

0.0119 

8.07694 

0.0901 

8.95488 

18 

0.0386 

8.58611 

0.1636 

9-21375 

58 

O.OI  1 7 

8.06932 

0.0893 

8.95104 

19 

20 

21 

0.0365 

8.56196 

0.1590 

9.20134 

59 
60 
61 

O.OI  1 5 

8.06184 

0.0886 

8.94726 

0.0346 

8.53908 

O.I547 

9.18960 

0.01 13 

8.05447 

0.0878 

8-94355 

0.0329 

8.51735 

0.1508 

9.17846 

O.OI  1 1 

8.04723 

0.0871 

8.93990 

22 

0.0314 

8.49665 

0.1472 

9.16787 

62 

O.OI  IO 

8.0401 1 

0.0864 

8.93631 

23 

0.0300 

8.47690 

0.1438 

9.15776 

63 

0.0108 

8.03311 

0.0857 

8.93278 

24 

0.0287 

8.45801 

0.1406 

9.14811 

64 

0.0106 

8.02622 

0.0850 

8.92931 

25 

0.0275 

8.43990 

O.I377 

9.13887 

65 

0.0105 

8.01943 

0.0843 

8.92589 

20 

0.0265 

8.42252 

0.1349 

9.1 3001 

66 

0.0103 

8.01275 

0.0837 

8.92252 

27 

0.0255 

8.40581 

0.1323 

9.12149 

67 

O.OIOI 

8.00617 

0.0830 

8.91920 

28 

00245 

8.38971 

0.1298 

9-11329 

68 

0.0 1 OO 

7.99968 

0.0S24 

8.91594 

29 

30 

31 

0.0237 

8.37420 

0.1275 

9.10540 

69 
70 
71 

0.0098 

7-99330 

0.0818 

8.91272 

0.0229 

8.35922 

0.1252 

9.09778 

0.0097 

7. 9  S  700 

0.0812 

8.90955 

0.0221 

8-34473 

0.1231 

9.09041 

0.0096 

7.98080 

O.0806 

8.90643 

32 

0.0214 

8.33072 

0.1211 

9.08329 

72 

0.0094 

7.97468 

0.0800 

8.90335" 

33 

0.0208 

8.31714 

0.1192 

9.07640 

73 

0.0093 

7.96865 

0.0795 

8.90031 

34 

0.0201 

8.30398 

0.1174 

9.06972 

74 

0.0092 

7.96270 

0.0789 

8.89731 

35 

0.0196 

5.29120 

0.1157 

9.06324 

75 

0.0091 

7.95683 

0.0784 

8.89436 

36 

0.0190 

8.27879 

0.1 140 

9.05694 

76 

0.0089 

7-95104 

0.0779 

8.89]  11 

0.0185" 

8.26672 

0.1124 

9.05082 

77 

0.0088 

7-94532 

0.0774 

S.S,sS?7 

38 

0.0180 

8.25498 

0.1 109 

<i"l  1-7 

78 

0.0087 

7.93968 

0.0769 

8.88573 

39 
40 

0.0175 

8.24355 

0.1094 

9.03908 

79 
80 

0.0086 

7-934" 

0.0764 

B.88293 

O.OI  71 

8.23241 

0.1080 

<).<>3344 

0.0085 

;.')-••»>- 

0.0759 

S.sson. 

a 

,    .6745 

.6745 
l/n=l 

j    .6745 

n 

•6745 

l/n(n— 1 

l    -6745 

•"74? 

j    -6745 
V  n—  1 

1       IIWI          1 

I    Vntn—\ 

l/nn-l) 

FORMULAS. 


(5) 
(6) 


(ii) 


(13) 
(14) 

(15) 


GENERAL  TRIGONOMETRIC  FORMULAS. 

(1)  sin  2«  +  cos  2«  =  1. 

( 2 )  sin  (a  ±  p)  =  sin  a  cos  p  ±  cos  a  sin  /J . 

(3)  cos (n ± /?)  =  cos  a  cos  /?  =f  sin  a  sin /?. 

tan  «  ±  tan  p 

(4)  tan(a±/?)  =  1_tanatan/j. 


sin  2  a        =2  sin  a  cos  a . 

cos  2  a        =cos  2a— sin  2a  =  1  — 2sin2a  =  2cosaa  —  1. 
2  tan  a 

(7)  tan2a        =i-tan*a- 

(8)  sin2a         =i(l  —  cos  2a). 

(9)  COS2  a  =J(1  +  COS  2a). 

sin  2a 

(10)  tana  =  1+^2^ 


sin  a+sin  /3  =  2  sin  £(a  +  /3)  cos  £(°  — £)• 


(12)  sin  a —sin  p  =  2  cos  Ma  +  Z3)  sin  J  (a 

COS  a  +  COS    /3  =  2C0SHa  +  J3)C0SHa  —  I3)' 
COS  j3  — COS    a  =  2sm%(a-\-(3)sml(a  —  P). 

sin2a— sin2/3  =  cos  2^—008  2a  =  sin(a-(-/3)sin(a — /?). 

(16)  COS  2a  —  sin 2  p  =  COS  (a  +  /?)  COS  (a  —  /?). 

„     sin  (a  ±  /?) 

(17)  tan  a  ±  tan  p  = 


cos 


^    _  sin  (a  ±  /?) 

(18)  COt  a  ±  COt    ^=±8inlsin7. 

(19)  sin  0  =  »-  I,  +|,  -  j ,  +  etc. 

^vj2  /^;4  /j«6 

(20)  cosa;  =  l-2i  +  Ij-gI  +  etc. 

FORMULAS  FOR   PLANE   TRIANGLES. 

In  these  formulas  a,  b  and  e  denote  the  sides  and  A,  B  and  C  the  opposite 
angles.  K  denotes  the  area  and  s  =  J(a  +  b  +  c).  Only  one  formula  of  each  set  is 
given,  the  other  two  may  be  obtained  by  advancing  the  letters. 

(>n  _£L.=:„6_-:r-°_ 

W  sin  A      sin  B     sin  C ' 

,o<n  q  +  6_tan}(4  +  Jg) 

(z/)  a  —  6  "tan  i(A—B). 

(23)  a2       =  b2+c2  —  2  6c  cos  J.. 

(24)  a        =6  cos  C  +  c  cos  5. 


(25)  sin  \A  =  J 


(s-b)(s—c) 
be 


exli 


142  FORMULAS. 


(26)  cos  I  A 


(48) 


(50) 


,52) 


Vs(s-a) 
~b~d 


(28)  Z"=£a6sin  C  =  \/s{s  —  a)(s  —  b)(s— c). 


FORMULAS   FOR   RIGHT   SPHERICAL   TRIANGLES. 

Denoting  the  right  angle  by  C,  the  formulas  are 

(29)  sin  a  =  sin  A  sin  e. 

(30)  sin  6  =  sin  2?  sin  c. 

(31)  tan  a  —  cosi?  tan  c  =  tan  J.  sin  6. 

(32)  tan  b  =  cos  A  tan  c  =  tan  B  sin  a. 

(33)  cos  A—  cos  a  sin  5. 

(34)  cos  B  =  cos  b  sin  4. 

(35)  cos  c  =  cos  a  cos  6. 

(36)  cos  c  —  cot  J.  cot  B. 

FORMULAS   FOR  THE  GENERAL  SPHERICAL  TRIANGLE. 

cos  a  =  cos  b  cos  c-\-  sin  b  sin  e  cos  A. 

(37)  sin  a  sin  B  =  sin  &  sin  A. 

(38)  sin  a  cos  B  =  cos  6  sin  c  —  sin  6  cos  e  cos  J.. 

(39)  sin  a  cos  C  =  cos  c  sin  6  —  sin  c  cos  b  cos  J.. 

(40)  sin  A  cot  J5  =  cot  6  sin  e —  cos  e  cos  4. 

(41)  sin  A  cot  C  =  cot  c  sin  6  —  cos  6  cos  J.. 

(42)  sin  J.  cos  b  —  cos  5  sin  C  -f  sin  5  cos  C  cos  a. 

(43)  sin  J.  cos  c  =  cos  C  sin  B  -f-  sin  C  cos  B  cos  a. 

(44)  sin  a  cot  6  =  cot  5  sin  C  -4-  cos  C  cos  a. 

(45)  *  sin  a  cot  c  =  cot  C  sin  5  +  cos  B  cos  a. 

(46)  cos  A  =  sin  B  sin  C  cos  a  —  cos  B  cos  0. 

Putting  s  =  H«+ &  +  e)  and  #  =  i(A  +B -f  C), 

(47)  sinM  =  ^J-n(*~bjsin(*-^. 

\  sin  6  sin  e 


«~,  i  j  /  sm  s  sin 

COS    J   A     =     =fc  ^    / ; — 

\     sin  6  ! 


(s -a) 
sin  c 


(49)  tanM  =  ±^ln 


sin  s  sin  (s  —a) 

Bin|a=±<1&c08^OB.(g-i4: 
\        sin  B  sin  6' 


(51)  cosJa  =  ±^-C08 


sin  ii  sin  C 


tanM  =  ±J— COS^COS('S~ 
\cos(Sf— 5)< 


cos  (S— C) 


(53)  sin  I  A  sin  J  (6  +  c)  =  db  sin  \  a  cos  J  (5  —  C). 

5  0  sin  £  .4  cos  J  (6+c)  =  ±  cos  \  a  cos  J  (5  +  C). 

1 55)  cos  J  ^1  sin  J  (6—  c)  =  ±  sin  i  a  sin  J  (5— C). 

cos  j  A  cos  J  (6  —  c)=  ±cos  J  a  sin  \(B  +  C). 

(57 1  tan'2  J  if  =  tan  £  8  tan  £  (s — a)  tan  J  (&• —  6)  tan  J  (s — c). 


FORMULAS.  143 

FORMULAS  RESULTING  FROM  THE  METHOD  OF   LEAST  SQUARE8. 

Formulas  for  Combining  Observations  and  Determining  Probable  Errors. 

1.  Direct  observations  of  a  quantity:   n  separate  results,   m1,m2,  .   .mn  of 
equal  weight. 

rmi    * 
Most  probable  value  of  quantity,  z  =— —  . 

Residuals,  z  —  m1  =  vt,  z — m2  =  v2, ...  z—mn  =  v„ . 

Probable  error  of  z ,  r0  =  ± 0.6745 A /  [vv\, . 

\  n  (n—i) 

Probable  error  of  a  single  observation,  r  =  ± 0.6745 ^  /  I  vv -1   . 

\  n  —  1 

2.  Direct  observations  of  a  quantity:   n  separate  results,  ml,m2,  ...nu  o* 
unequal  weights,  p1 , p2 ,  . .. p„. 


Most  probable  value  of  quantity,  z  = 


Probable  error  of  z ,  r0  =  ± 0.6745  A /    [P^PL , 

V  \p\  (w— 1) 

Probable  error  of  an  obs'n  of  weight  unity,   r  =  ±0.6745       IPVV  i  . 

Weight  of  z,  P  =  \_V\ 

Relation  of  weights  to  probable  errors,  px  :p0 :  . '.  : :  — ?  :  —2  ■  ■  ■ 

3.  If  Z  =  a^  ±  62g  d=  . . .  &?» ,  and  the  probable  errors  and  weights  of  zlyz2, ..  .z* 
are  rltr2,  ...  r„  and  px,p2,  ...p„,  then  the  probable  error  and  weight  of  Z are  given 
by 


r=±i/(ar1)2  +  (6/2)*  +  ...{krn  f. 
1   _  g»       6"     .        ^ 

4.     In  general,  if  £  =/  (^ ,  ^ ,  ...  2»),  the  probable  error  of  Z  is 


••W(f)WlC)W...+(iDV,. 

5.  Direct  observations  of  a  function  of  a  quantity  z:  the  separate  results, 
mi ,m2, . . .  m„  of  equal  weight,  and  the  form  of  the  function,  az.  The  observation 
equations  are 

o\  z  +  mj  =  0 , 

a2  0  +  m2  =  0 , 

anz  +  m„  =  0 . 
The  most  probable  value  of  z  and  its  probable  error  are 


Z=-W  r  =  ±0.6745  J il^J_ 

[aa]  \  [aa]  (n  —  l)- 

If  the  observations  are  of  unequal  weights,  multiply  the  observation  equations 
through  by  the  square  roots  of  their  respective  weights,  and  proceed  as  before. 

6.    Direct  observations  of  a  function  of  two  quantities,  w  and  z  :  the  separate 

*The  symbols  [  ]  signify  the  sum  of  all  similar  quantities.    Thus, 
[m]  =Tni  +  m2+  ...  +  m„  . 
[puu]  =  pi.Vi2  +p2t>22+...  +P»f»2. 


1  J  I  FORMULAS. 

results,  /«! ,  m2,  ...  m„  of  equal  weights,  and  the  form  of  the  function,  aw-\-bz.    The 
observation  equations  are 

ax  w -\- bx  z  -\- m1  =  0, 

a2  w  +  bs  z  -f-  m2  = :  0 , 


a„  w  -f-  b„  z  +  ra„  =  0 . 

The  normal  equations  are 

[aa]w+[ab]z-\-[am]  =  0  , 
[ab]w  +  [bb]z+[b?n]  =  0. 
Let 

Then  the  most  probable  values  of  w  and  z  are  given  by 

Z~       [65.1]' 

[  a  6 1         [am] 
[aa]        [ oa] 
The  weights  of  w  and  2  are 


p.  =  [66.1],  i>«  =  -[y^J[a«]. 


The  probable  error  of  a  single  observation  (of  weight  unity)  is 

r=  ±0.6745  A/S3; 
\  n— 2 

and  the  probable  errors  of  jo  and  z  are 


If  the  observations  are  of  unequal  weights,  multiply  the  observation  equations 
through  by  the  square  roots  of  their  respective  weights  and  proceed  as  before. 

7.  Direct  observations  of  a  function  of  three  quantities,  x,  y  and  z\  the 
separate  results.  m1,m2,  ...mn  of  equal  weight,  and  the  form  of  the  function, 
ax  +  by  +  cz.    The  observation  equations  are 

«!  x  -f  6X  y  +  cx  2  +  raj  =  0 , 
a2  a?  +  &2  2/  +  c2 z  +  mi  —  0 , 


anx-\-  bnyJrc„z-\-m„  =  0. 
The  normal  equations  are 

[aa]a;+[a6]y  +  [ac]2  +  [ara]  =  0, 
[a6].r  +  [66]2/  +  [6c]z+[6m]  =  0, 
[ac]a?-j-[&c]2/  +  [cc]2  +  [cm]  =  0. 


Let 


[&&3-[a£]  [«&]=[&M],     [^]-[-^L«c]=[6c.l], 
f  6  ml  — ^ — ^  [  a  m  ]  =  [  6  m.\  ]  , 

l'rc-1]-[w!L?"r-1]  =  c""-2]'   [^•i]4^;i][6w-1]  =  rcw-2]- 


FORMULAS.  145 

Then  the  most  probable  values  of  x,  y  and  z  are  given  by 

_[em!2] 
z~      [cc.2]' 

_[6c.l]         [5m.l] 
*  [66.1]  [6  6-1  1  * 

[  «  &  1  y      [^L_,J>wJ. 
[aa]  [aa\        [a  a] 

The  weights  of  x,  y  and  z  are  given  by 

p„  =  [cc.2], 

^*       [  e  c.l  ] L  J 

Px        [eel];   [66  ]L       J' 
in  which 

The  probable  error  of  a  single  observation  (of  weight  unity)  is 

r  =±0.6745  JE3. 
\  w  —  3 

and  the  probable  errors  of  #,  y  and  z  are 

_     r  ,  _     r  ,  _     r 

If  the  observations  are  of  unequal  weights  multiply  the  observation  equations 
through  by  the  square  roots  of  their  respective  weights,  and  proceed  as  before. 


CONSTANTS. 


Mathematical  and  Astronomical  Constants. 

log. 

Base  of  natural  logarithms e=  2.71828183  0.43429448 

Modulus  of  common  logarithms ^  =  0.43429448  9.63778431 

Radius  of  a  circle  in  degrees f  =  57-29578  1.75812263 

"      "minutes r.=  3437.7468  3.53627388 

"         "       "      "seconds r  =  206264.806  5.31442513 

Circumference  of  a  circle  in  degrees 0  =  360  2.55630250 

"               "       "      "  minutes 0  =  21600  4-33445375 

"               "       "      "  seconds 0=1296000  6.11260500 

Sine  of  one  second 0.000004848137  4.68557487 

ir  =  3.14159265  0.49714987 

-  =0.31830989  9.50285013 

fl"8  =  9.86960440  0.99429975 

l/jT  =  1.77245385  O.24857494 

-y  g-=  0.80599598  9.90633287 

Mean  solar  days  in  a  Julian  year 365-25  2.5625902 

"        "        "       "    sidereal  " 365-25637  2.5625978 

"         "         "       "    tropical  "      365.24222  2.5625809 

"         "         "       "    sidereal  day 0.99726957  9.9988126 

Sidereal         "       "    mean  solar  day 1.00273791  0.0011874 

Number  of  seconds  in  a  day 86400  4.9365137 

"        "         "           "    sidereal  year 31558150  7.4991115 

Square  root  of  the  attractive  force  of  the  sun  (Gauss)  k  =  0.01720210  8.2355S14 

"        "       "             "            "        "        "    in  see's  k  =  3548.18761  3.5500066 
Time  required  for  light  to  traverse  the  distance  from 

the  earth  to  the  sun 4q89-57  2.6977261 

Equatorial  horizontal  parallax 8". 80  0.9444827 

Aberration  constant 20  ".52  1.3121774 

Nutation  constant,  according  to  Peters 9".2236  +  o".ooooo9  (t— 1850). 

General  precession,  according  to  Struve 50^.2524  +  0  ".0002268  (t— 1850). 

Precession  constants  for  the  equator,  accord- )      \m  —  46\o76s  -f- 0^.0002849  (t — 1850) 
ing  to  Struve  and  Peters,  (tropical  year,)  f      {  n  =  2o".os64  — o".oooo863  (t— 1850). 
Obliquity  of  the  ecliptic,  according  to  Struve    .... 

230  27'  30". 76  —  o".473S  (t — 1850)  —  o".oooooi4  (t — 1850)*. 

Comparison  of  Linear  Measures 

log. 

1  English  inch 0.02539977  metres  8.4048298 

1        "       foot 0.30479727       "  9.4840111 

1        "       yard 0.91439180       "  9.961 1323 

1  metre      3.28086933  English  feet  0.5159889 

1  centimetre *  0.39370432       "       inches  9.5951702 

1  toise  =  6  Paris  feet 1.94903631  metres  0.289S199 

1  Paris  foot  =  1 2  Paris  inches 0.32483938       "  9.5116687 

1  Paris  inch  =  12  Paris  lines 0.02706995       "  8.4324874 

1  Paris  line 0.00225583      '  7.3533062 

CXlvJ  *  From  fMarki-'s  Comparison  of  lSiHi. 


CONSTANTS. 


147 


Dimensions  of  the  Earth  according  to  Bessel  loo. 

Equatorial  semi-axis a  =  20923597.  feet  7.3206363 

3962.8025  miles  3.5980024 

6377397.15  metres  6.8046435" 

Polar  semi-axis b  =  20853654.  feet  7.3191822 

3949-5557  miles  3.5965482 

6356078.96  metres  6.8031893 

Compression.    .     .       p  =  -~  =  2q9-I528  =  °-°°3342773  7.5241069 

Eccentricity 6  =  0.08169683  8.9122052 

Quadrant  of  a  meridian Q  =  10000855.76  metres  7.0000372 

Dimensions  of  the  Mirth  according  to   Clarke  (1866).*  ]ocr 

Equatorial  semi-axis a  =  20926062.  feet  7.3206875 

3963.3  miles  3-598o536 

Polar  semi-axis b  =  20855 121.  feet  7.3192127 

3949.8  miles  3. 5965788 

Compression p  =  2Q,Q7s4  =  °-°°339oo79  7-5302098 

Eccentricity 6  =  0.08227189  8.9152515 

Circumference  of  Equator =  24901.96  miles  4-3962335 

Perimeter  of  meridian  ellipse =24859.76      "  4-39549°9 

Area  of  the  Earth's  surface =1 96940400  square  miles. 

Constants  for  Conversion  of  English    Weights  and  Measures  to  Metric,  and 

vice  versa.* 

LINEAR. 

I  inch  =  2.54001  centimetres.  I  centimetre  =  0.393700  inches. 

I  foot   =  0.304801  metres.  1  metre  =  3-2S°83  feet- 

I  yard  =  0.914402      "  I      "  =  1.0936 1  yards. 

1  mile  =  1.60935  kilometres.  1  kilometre    =  0.62137  miles. 

1  nautical  mile  =  6080.27  feet  =  1.1516  statute  miles  =  1-85325  kilometres. 

SQUARE. 

I  square  inch  =  6.4516  square  centimetres.  1  square  centimetre  =  0.15500  square  inches. 

I  square  foot  =  0.0929  square  metres.  1  square  metre  =  10.7639  square  feet. 

1  square  yard  =  0.8361        "  "  I       "  "  =  1. 196  square  yards. 

1  square  mile       2.5900  square  kilometres.  1  square  kilometre    =  0.3861  square  miles. 

I  acre  =  0.4047  hectares.  r  hectare  =  2.4710  acres. 

I  square  mile  =  259.008       "  I  square  mile  =  640  acres. 

CUBIC. 

I  cubic  inch  =  16.3872  cubic  centimetres.  1  cubic  centimetre  =  0.06102  cubic  inches. 

1  cubic  foot  =  0.02832  cubic  metres.  1  cubic  metre  =  35.3145  cubic  feet. 

I  cubic  yard  =  0.76456     "  "  I      "        "  =  1.3079  cubic  yards. 

CAPACITY. 

I  fluid  dram  =  3.70  cubic  centimetres.  I  cubic  cm.  =  0.27  fluid  drams. 

1  fluid  ounce  =  29.57     "  "  1  "        =  0.0338  fluid  ounces. 

1  quart  (XJ.  S.)        =  0.94636  litres.  I  litre  =  1.0567  quarts  (U.  S.). 

I  gallon  (U.  S.)      =3-78543     "  I     "  =0.26417  gallons  (U.S.). 

I  bushel  (U.  S.)     =  0.35239  hectolitres.  I  hectolitre  =  2.8377  bushels  (U.  S.). 

I  gallon  (British)   =4.54683  litres.  1  litre  =  0.21993  gallons  (British). 

I  bushel  (British)  =  0.36348  hectolitres.  1  hectolitre  =  2.75121  bushels  (British). 

*  Adopted  by  the  U.S.  Coast  and  Geodetic  Survey. 


I  kilogramme 
I           " 
I           « 
I           " 
I  tonne 

=  35-2739  oz-  avoir. 

=  2.20462  lbs.     " 

=  32-1507  oz.  Troy. 

=  2.6792  lbs.     " 

=  1. 1023 1  tons  of  2000  lbs. 

I     " 

=  0.98421       "      2240  lbs. 

148  CONSTANTS. 

I  Imperial  gallon  (British),  (1&90)  =  277.463  cubic  inches. 
I  gallon  (U.  S.)  =  231.  "         " 

I  bushel  (U.  S.)  =2150.42       "         " 

WEIGHT. 

I  grain  =  0.0647989  grammes.  1  gramme         =  15.4324  grains. 

I  oz.  avoir.  =  28.3495  " 

I  lb.      "      (=  7000  grs.)  =  0.45359  kilog. 

I  oz.  Troy  =  31.10348  grammes. 

I  lb.     "     (=  5760  grs.)  =  0.37324  kilog. 

1  ton  of  2000  lbs.  =  0.907186  tonnes. 

I       "      2240    "  =  1. 01 605         " 

VELOCITY. 

I  foot  per  sec.  =  0.6818  miles  per  hour  =  1.0973  kilometres  per  hour. 

1.4667  feet       "        =1  mile         "  =  1.6093  "  " 

O.91 13    "         "         =  0.6214  miles        "  =1  kilometre         " 

I  metre  per  second  =  2.2369  miles  per  hour. 

FORCE,  (g  =  981  cm.) 
Weight  of  I  gramme  =  981        dynes.  1  dyne  =  weight  of  0.001019  grammes. 

"         1  grain      =63.57        "  1      "    =         "  0.01573  grains. 

I  poundal  =  13825.5    "  1      "    =  7.2330  X  10    5  poundals. 

STRESS. 

I  lb.  per  sq.  inch  =  70.307  gms.  per  sq.  cm.       I  gm.  per  sq.  cm.  =  0.01422  lbs.  per  sq.  in. 

I       "      "      foot  =  4.8824  kg.       "         "  1  kg         "        m.  =  0.20482    "         "       ft. 

I  standard  atmosphere  =  1033  gms.  per  sq.  cm.  =  14.7  lbs.  per  sq.  in. 

WORK. 

I  foot-poundal  =  421403  ergs.  1  erg  =  2.3730  X  io- 6  foot-poundals. 

I  joule  =  io7  "  1  megalerg  =  1  o6  ergs. 

1  foot-pound  (9  =  981  cm.)  =  1356.3  X  io4  ergs  =  0.138255  kilogramme-metres. 

I  kilogramme-metre  (g  =  981  cm.)  =       981  X  io5  ergs  =  7.2330  foot-pounds. 

RATE    OF    DOING   WORK. 

I  horse-power       =  746  watts  =  1. 01387  force  de  eheval. 

I  force  de  eheval  =  735!     "      =  0.98632  horse-power. 

I  horse-power        =  33000  foot-pounds  per  minute  (g  =  981  cm.) 

I  watt  =  44.2385       "  "  " 

1  force  de  eheval  =  75  kilogramme-metres  per  second        " 

TIIYSICAL    CONSTANTS. 

I  cu.  inch  of  distilled  water  at    40  C.  weighs  252. 56S  grains  =  16.3662  grammes. 
I         "  "  "  620  F.      "        252.286      "      =  16.3479         " 

I  cu.  foot      "  "  620  F.      "        62.2786  lbs.  avoir. 

1       "        of  dry  air  320  F.,  pressure  760  mm.,  weighs  565. 1  grains. 

1  litre  "        "  o°  C,        "  "  "        1.29305  grammes. 

Acceleration  of  gravity  at  the  sea  level  for  the  latitude  (ft  (Harkness), 
in  feet        per  sec,  g  —  32.0S6528  -f  o.  171 293  sin'2  (j>  ; 
in  metres  per  sec,  g    -    9.779886  1-  0.052210  sin'2  <£. 
Value  of  g  al  equator  =  9.7799  m.  per  sec;  at  poles  =  9.8321 ;  at  Greenwich  =  9.81 17: 

ii  Paris  =  9.8094;  at  Washington  =  9.8007. 
Length  of  seconds  pendulum  at  sea  level  for  latitude  (p  (Harkness), 

1=  39.012540  +  O.208268  sin'-;  (j>  inches  =  0.990910  +  0.005290  sin'2  (p  metres, 

Velocity  of  lighl  in  vacuum,  according  to  Newcomb, 

[86326  miles  per  Becond  =  299860  km.  per  Becond. 
Velocity  of  sound  in  dry  air  =  1090  \/i  +  0.00367  /°  ('.  Eeel  per  second. 


25  16  3  9  fl 


14  DAY  USE 

RETURN  TQ.DESI^fRQM  .WJHXCH  BORROWED 


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